NOTE: These are theories. I am not a firearms expert. I am bad at tactics. However I am good at imagining and extrapolating, and that's exactly what's happening here - guessing.
Edit: 4hrs after original post.
The first thing I think of is that distraction grenades suddenly become a lot cheaper because you wouldn't have to make them as loud. Silly, right?
A certain thing is that tactics would change. The question is how much.
First of all, firefights would be much quieter. Every soldier now has the silence, if not the range, of a sniper now. 400-800 meter battles are common, as all the army has to do now is add a sight to the rifle to make it (more) lethal at range. Urban Street warfare probably won't change too much. Foot soldier adoption may be prevalent at first, but I think that it'll eventually become necessary for all soldiers to have one to even be effective in the battlefield.
Common rifles used by the US military are the M16A4 and the M4A1. There is a rumor around that the M4A1 could soon achieve groupings of 5" at 600m. This would allow near-silent warfare at 400m, and the only indication that someone is shooting at you comes from the sound of the bullets flying by and hitting stuff - and possible your mates dying.
I can see the creation of an entirely new kind of warfare that I do not feel confident predicting. Or maybe it becomes an extension of modern/guerilla warfare.
Another thing I can see happening is that this improvement is too radical, and if the company making it is based entirely in one country (say the US or China or (WWII)Germany) then there might be an export ban and information ban with high treason as consequence. However, I could also see that if there was an active war on, the suppressors would be looted from dead enemies for a reward and then reproduced by the enemy anyway. If there wasn't a war on, then they would trickle out through the black-market.
But wait! There's more!
The ability to suppress sound like that with something so simple requires a radical shift in the understanding of how sound works and more importantly - how to model its creation, propagation, and perception.
Sound artists today live in the stone ages. They are basically at the equivalent of drawing cartoons on a sheet of paper before scanning them into a computer to touch them up. And that's rather bad when we consider that the graphics in video games are 100% computationally generated ON THE FLY.
The problem with sound is that it is light, but everything is a mirror. And humans can be as accurate at telling where something is with sound as light (while Joe Normal is not). So getting it right is kind of important. Mix that with the fact that humans hear a much greater range of sounds than they can see wavelengths, and it's a doozy to model.
This is important because for a consistent reduction in dB downrange to 50, the knowledge of how the sound exits the gun has to be perfect. And that's going to change from gun to gun. So basically what you have is a dynamic suppressor.
There are a few ways I can think of to do this off the top of my head. Nanobots (the easy way out) or a nano material that changes its reflectivity of sound waves based on x (x being something like electric potential or deformation or pressure). The second idea would probably need either sensors inside the gun or sensors on the gun - something to predict how the sound is going to cascade through the suppressor this particular time.
How the suppressor would work is it would cascade the sound waves in such a way that the waves that exit the end of the suppressor collide in near-perfect interference. That's hard because all of the different frequencies need to be matched with each other and phase-shifted by half a period. You need to take half the wave and delay it by how fast it's going times how long the wavelength is. If you do this purely geometrically (which is how silencers today work), then you don't have to worry about how fast the sound is traveling. But, like the shot of a sniper, the more precise you want to be, the more variables you need to take into account.
Advances are being made in how we generate sounds. Auto-tune is an old example of this. But that's hard because there's a lot of different materials with a lot of different properties that all make different sounds based on how they are making contact.
So the fact that this "ideal suppressor" exists means that not only are movies and interfaces going to be so much better than before, but we actually have a system for finding out how surfaces reflect/refract sound in a way that can be used to make better friction approximations. And magnetic friction approximations. And model brain activity. Model the atmospheric situation of the planet(s) better. So much cool stuff.
So yeah. If this was a thing in WWII, then my prediction would be that there would be some drastic changes to how humans live. Or if they live.
EDIT 2: Thanks to ohwilleke for pointing this out.
There is a third way to achieve an ideal suppressor - speakers. Most people would say that putting a half-pound of speaker on the front of a rifle is nonsense for an infantryman. But if the speaker was powered by piezoelectric crystals and wired with simple sensors (more piezoelectric crystals) and a waveform inverter (ridges become troughs and vice versa) then with the right geometry of speaker, excellent cancellation becomes viable. The cool thing is that the mechanical component of the suppressor already has a lot of the requirements for this kind of thing.
- High Pressures
- High Surface Area
- 1-Dimensional Cancellation (we don't want people down-range to hear us)
- Low Load Times
And the active suppressor is taking energy harvested from the passive suppressor so that the passive suppression works better. The reason this would work on broadband sound is that the cancellation is in concert with the noise, so the speaker doesn't care what frequency it is. Geometrically, what's happening is that the speaker is listening to a bunch of $sin^2$ waves all permuted and phase shifted. So all you do is take the loudest sound in a shot and make that 1. Then you subtract the loudness of the current sound, and have the speaker emit the rest.
It's actually a lot more complicated than that (which is why ideal suppressors don't exist yet), but I think that's enough to get the gist of it.