I need a reason for two antagonistic humanoid lifeforms living on the same planet to be completely incapable of direct physical contact.
I don't mean they have a strong aversion to it, I mean they literally should be unable to on a fundamental, physical level.
This already basically exists on earth. Ever touched a live deep-sea fish (one that is born and lives its entire life in the deep sea)? Nope, and you never will. The pressure they live in would kill us instantly and the pressure we live in would kill them instantly. Our two species will never, ever touch each other while alive.
Generalizing, a few things together create a situation where they two species cannot touch:
This works because I assume that we don't count touching corpses or touching through a spacesuit kind of thing. Also, if you want to prevent even touching corpses, you'd have to add that the environments also instantly dissolve/obliterate the inhabitants of the other environment (kind of like the matter/antimatter idea which seems prevalent so far.) If you want that, you've gone beyond the scope of "already exists on Earth", but anti-matter+matter could still do it for you.
I like this reason because it also gives a very solid reason for the two species to be antagonistic - their living space is exactly the opposite of the other species' living space, and if one side manages to spread its environment totally, it will mean the utter annihilation of the other species.
Now, to be fair, it's not a guarantee that deep-sea fish will explode in our pressure. That's okay - we just need them dead, we don't need spectacularly dead.
One of the species is an evolutionary descendant from the future of the other species. They have invented time travel, and the universe is one where "the universe guarantees paradox-free time travel". This means that there will be subtle changes in randomness that will steer any process away from a path that would cause a paradox.
This future species also carries a future disease that is transmitted on touch. If they would touch the other species, it would lead to grandfather paradox - and the universe won't permit it.
Psychrophiles and hyperthermophiles
While on Earth, the majority of hyperthermophiles are archae, there is no reason sufficient evolution in another environment wouldn't result in humanoid hyperthermophiles. If one species is a psychrophile, it could easily survive in sub-zero temperatures, but will die within seconds, or instantly, if the temperature gets above -10 C. The other species, a hyperthermophile, can survive in extremely high temperatures, and anything under 100 C will kill them. There is no overlap in survivable temperatures, no common ground on which they can meet.
Ionizing adiation
There are some organisms that feed on ionizing radiation. There are other organisms that produce enzymes which use ionizing radiation to repair damage (such as the enzyme photolyase). If one species evolves in an environment with such extreme radiation that blocking the radiation is impossible, then they may very well end up depending on that radiation for whatever reason (or perhaps they generate it themselves, and instead of filling themselves with lipids in fat as we do, they fill themselves with radon). The other species simply has to have evolved in an environment with extremely little radiation, far less than we are exposed to. They would evolve with very few, or no, biological mechanisms to repair genetic damage caused by radiation. Each species would die quickly in the other's environment.
Electric fields
Electric eels can create lethal currents to incapacitate or kill potential predators and prey. They are able to regulate the amount of electricity they produce, but this is not limited by physics. If a species were to generate high levels of electricity under nominal conditions (whether as a byproduct of their metabolism, an evolutionary protection mechanism, or any other reason), then it could be lethal for a different species to touch it. This could be extended to making close proximity lethal by having the other species highly sensitive to magnetic fields, e.g. by evolving with similar properties to modern electronics. Perhaps both species are cyborgs, where one of them produces a powerful electric field in order to function due to having evolved in conditions where extremely high power outputs are required, and the other is extremely sensitive to electric fields, as they could crash its internal vital components. If this species evolved in an environment where power conservation was vital, they would be using low-power components that are especially vulnerable to this.
Byproducts of metabolism
Cyanogenic bacteria are microorganisms that produce cyanide (CN-). This is extremely lethal to us, because it jams our vital metabolic machinery. If one humanoid evolved to produce high levels of a toxic gas (and had to get rid of it rapidly, preventing them from simply "holding it in"), they could not get anywhere near another humanoid species without killing it. If a cyanogenic organism our size were even in the same building as a human, we would die before even being able to escape. You could make it impossible for one species to even get close enough to touch the other by having each produce a mutually lethal gas, as they would mutually kill each other before getting close enough to touch.
Explosive-reactive skin
Modern tanks are coated with so-called explosive-reactive armor. This is a type of armor which explodes violently outward if it is punctured or hit, with the goal being to deflect, melt, or decelerate anti-tank projectiles. If one species had skin coated in a chemical that reacts violently when in contact with a chemical that coats the other creature's skin, physical contact would be impossible, as it would result in both creatures being blown away from each other, and possibly killed. Since you did say they have to be on the same planet, this can't be something as extreme as matter vs antimatter, as they could not coexist at any significant level on the same planet.
Enemy symbionts
Symbiotic relationships are common in nature. Imagine a scenario where one humanoid is surrounded by a symbiotic insect that protects and nourishes them, but would attack and kill the other species. It would be impossible for one species to get even close to the other without one of them dying, and it could very well be impossible to even temporarily get rid of the insects if their relationship involves obligatory symbiosis.
The two humanoid lifeforms are two mental states inhabiting the same bodies. The switch is triggered, for instance, by the day/night cycle, or it follows a seasonal pattern. All the planet is simultaneously in the same mental state, so that they can never touch a body in which the mind is in the "other" mental state.
In a fictional world just like in Stranger Things' upside down or Stanislav Lem's amazing Futurological Congress; living species in different dimensions sharing exactly the same location at the same time may not contact each other physically. The reason why such dimensions occur or how the gateways work is speculative.
I'd like to suggest improvement for the idea about the magnetic forces. In this variation the humanoids of species A are enormously strong magnets and the humanoids of species B are simply paramagnetic. As such, they will demonstrate an effect similar to magnetic levitation when they meet (see picture with a frog floating in the magnetic field).
Otherwise I don't see real world long range forces that can explain something like this. Gravity can only attract, but not repel, electricity only has two charge signs, so it's not possible to imagine any three individuals interacting as described, and atomic forces have very short range (though Lennard-Jones potential, if you wish, is a proof that even humans can't touch each other - atoms can't be pushed together, it takes huge particle accelerator to do that).
Having said that, I'd like to add that a concrete wall between them will be better explanation than magnetism.
Different types of species preservation that does not affect their own species. One species emits an electric field that will kill the other species. and the other species a poisonous skin emission or vapor (toxic gas) as part of their metabolic process or they might even have psychic defenses adapted over the millennia of which the opposite species is sensitive to.
You did not say if both originated on the planet so it is possible one species migrated from off world maybe when the planet was young and there were few of the other humanoids already there. The species from off world may have crashed on the planet and never encountered the other species until the population had grown sufficiently, so they would have different evolutionary paths.
Or going along with Brian Rogers post below, they could have organic secretions that when combined create a reactive substance that would kill both individuals. Separately benign, combined super enriched poison ivy oil.
One species evolved in colder climates developing an antifreeze like substance in their blood that keeps them from freezing in the super cold climate, but their bodies cannot tolerate the temperatures in the equatorial regions. Likewise the ones that evolved in the equatorial regions cannot tolerate the subzero cold in the polar regions.
Different altitudes, one breathes thin atmosphere, the other breaths thick moist air or has some chemical in the lower atmosphere needed for their metabolism, maybe given off by plants that only grow at low altitudes.
There may be a toxin in one environment that one species has not only adapted to, but is now required to live, while the other species is still susceptible to the toxin. Maybe high amounts of methane in a swampy environment or something along those lines.
Matter/Antimatter
We have currently the problem why antimatter which behaves exactly symmetrical to matter seems to be missing in this universe (We can create it, but only very tiny amounts).While it is possible that some galaxies could be made from antimatter, it seems unlikely because once matter and antimatter are in contact, both decay into light with 100% efficiency. Touching is therefore impossible, but even a separate Galaxy should emit detectable light because space is not entirely devoid of matter.
The other species live in a mirror universe and we both travel with wormholes between the universes. We can only enter the other universe in space because contact triggers an explosion approx. 100 times stronger than a hydrogen bomb. That means contact between two human-sized beings would level New York...the state. Space is empty enough so that a spaceship would be surrounded by harmless flashes.
For some reason your aliens developed a strong magnetic field that they are constantly emitting.
Your humanoids use this to attract prey, either by forcing them directly through the magnetic field influencing the prey's body or by for example foiling their orientation. The prey tries to walk or fly around normally and suddenly their organs are telling them to go straight to their right, into the arms of the waiting humanoids. Look at birds and their Magnetoreception.
Because they both evolved this mechanism they now repel each other.
They are hermaphrodites that reproduce by direct contact with each other. In their reproduction cycle, if 2 organisms touch, they inject each other with genetic material and then both will die off in the process of creating offspring.
I think the easiest way to do make physical contact impossible is for one (or both) species to evolve beyond the corporeal state. Your species might even be subspecies rather than independent species. Moreover, the story can be scientifically plausible.
For example, several centuries ago your humanoids finally managed to upload their minds to a global network. Half of the population decided to abandon their bodies and continue existence in a digitised form. The other half, 'naturalists', opposed them claiming that this decision goes against everything humanoids stand for...
The Great Schism led to a long war with countless victims. But eventually, there were no more 'digitisers' left that could be killed. 'Naturalists' went back to 'natural and sustainable' lifestyles, while 'digitisers' enjoy their perfect virtual reality. However, they still hate each other, even though even virtually immortal 'digitisers' are starting to forget what was all the fuss about...
They both live in swampy environments, each exudes a delightful-smelling musky lubricant that allows them to slither through their environment and protects them from contact with the potentially nasty things that live there - and each species slime is both disgustingly stenchy and a deadly toxin to the other species. Contact = mutual death.
What about a humanoid praying mantis type species of aliens that live on a planet that has two, stay with me here, "Dyson-like hemispheres" that compartmentalize the planet into two sections for male and female to keep the females from killing the males, and where breeding is done underground and contracted through a bureaucratic alien species like that of the Vogon. Also, a transgender narrative within this praying mantis species could play well with the emotions evoked in the current climate surrounding acceptance of transgender individuals, particularly with this kind of black-and-white compartmentalized form of life. Like, a rogue transgender mantis within the female hemisphere society who wants to be male. There is a lot of play in a storyline similar to that.
They exist in different quantum states where they could be physically in the same place but out of phase with each other. They appear to the other as a ghost at the most or not at all.
Possibly one is composed of dark matter and the other normal matter, and the planet itself is composed of both type of matter superimposed over each other.
Very strong allergic or auto-immune reaction
It should be enough that sweat or other chemicals on skin of one of the species causes a violent allergic reaction in the other species.
Think any allergy that occurs by contact with mucous membranes (or equivalent in your species), eg. https://en.wikipedia.org/wiki/Latex_allergy but much stronger and possibly deadly. Strong enough that noone would risk touching.
It can be of course mutual. For example consider it's deadly to transplant blood of type A to a patient with blood of type B, and vice-versa. It should be enough that both species cause a strong self-immune or allergic reaction when they touch.
A 3rd alien species has a zoo planet. They are predator and prey so alien #3 has erected walls, ceilings, and defenses to keep them apart. Possibly to study them.
Their bodies are in chambers and they are in holodecks. They can see each other, but they can't actually touch. If you want to go the extreme the holodeck can be programmed to keep at least 2mm space between people therefore touch is impossible.
It happened already in one sci-fi tale: a girl from a planet, where the life based on ammonium and a boy from the expedition from a water planet. They could only speak to each other, through a glass/microphones. They dreamed that they would find a planet, where the temperature, would be cold but acceptable for him, and hot but acceptable to her. But -90C is too much cold for him and too hot for her. And they only gave each other a farewell kiss, that burnt the lips of they both. Romeo and Juliet, that really can't meet in body. A sad story.
I would propose a girl and a boy that live in different Galaxies of which each is build of antimatter to another. They got acquainted by radio (photons are neutral), and if they only try co close, a strong flash brighter than a star appears for a moment... Take for sure, these two cannot touch each other.
Depending on how they evolved, which I would assume would be relatively distant from each other, you could have the two harbor different symbiotic bacteria on their skin, that on contact, results in an almost flesh-eating like disease for both, or at least some bad skin irritation.
The two species coevolved in an environment with intense competition. One of the species evolved an instinctive and entirely uncontrollable reflex where when they sense a pheromone produced by the other, they exhale a venomous substance that is fatal to the other species, but tolerated by their own kind.
I would propose them live in different Galaxies of which each is build of antimatter to another. They got acquainted by radio (photons are neutral), and if they only try co close, a strong flash brighter than a star appears for a moment... Take for sure, these two cannot touch each other.
