Short answer no, long answer probably no, but...
Any reactor of our current designs not actively managed by humans, even when shut down, will eventually suffer an accident, either from the spent fuel pool running dry or the reactor itself from decay heat. The Fukushima accident didn't happen with active reactors; they were shut down but still hot due to decay heat.
If, at any point in that 150 years, the core becomes uncovered, it will likely meltdown and, depending on whether an ignition source is present, explode due to hydrogen formation when its fuel's zirconium cladding gets too hot.
So more than likely the bigger problem is there won't be any abandoned reactors for your mutants to find.
However, if they somehow have no problems with radiation, and possess the appropriate knowledge, building a new reactor would be almost trivial.
The first reactors, called uranium piles, were little more than their names suggest: A pile of uranium and graphite as a moderator. The first was assembled and run without any shielding under the stands of the football field at the University of Chicago.
All your mutants will need to do is gather up enough natural uranium, form it into fuel rods (which might be difficult, since uranium is an extremely dense and hard metal), and assemble it with an appropriate moderator.
So what is an appropriate moderator? Well for natural uranium that would be heavy water or graphite. Heavy water is extremely difficult to produce and requires modern industry and technology, so you'd be stuck with graphite, which is also somewhat difficult to produce, but far easier than heavy water, and could conceivably be done by any society that has the technology to process uranium ore.
This ultimately means building the core becomes the easy part. The hard part? Getting a turbine and creating the cooling and heat exchange system.
Turbines require extremely balanced blades and very precise engineering. They're one of the most expensive parts of any power plant, nuclear plants included. This means they'll probably be out of reach for your post apocalyptic society. However, this is where your abandoned nuclear plant comes in.
Modern civilian reactors in the United States broadly fall into two categories: Pressurized water reactors and boiling water reactors.
In a PWR, the water is kept under extreme pressure and its heat is exchanged with a second isolated cooling loop to produce steam. This steam then drives the turbine. Unfortunately, the technology required for a PWR is almost certainly beyond your mutants, but all hope isn't lost.
In a BWR, the water is converted directly to steam in the core, then used to drive the turbine. This steam is weakly radioactive, and so makes the turbine slightly radioactive, which is one reason BWRs have fallen out of favor (but they still exist, and indeed Fukushima's reactors were all the BWR design). However, this direct conversion attribute of the BWR means it will be more within reach of your mutant nuclear engineers.
Let's go with the following scenario: Your mutants stumble across an abandoned nuclear plant that was never completed. Let's say it has its turbine and electrical infrastructure in place, but the boiling water core was never completed.
The reactor pressure vessel for the original reactor is on site in the reactor room, but was never completed. It has no fuel or control rod infrastructure, but the piping is hooked up. For all intents and purposes, it is a large, empty metal basin capable of holding water. The concrete containment structure also hasn't been completed, but that won't matter to your radiation resistant mutants.
Your mutants happen to have a bookworm among them who has spent her life studying artifacts and books from the past, and has a very good understanding of engineering principles, but no ability to actually create any of the technology she knows about. She correctly deduces the plant's purpose and technology, and has enough of an understanding of nuclear physics to at least, in theory, understand how to build a rudimentary uranium pile.
Realizing how precious and valuable this lost technology is, your mutants establish a colony at the plant and decide to complete it, presumably to generate power for society and attempt to help reestablish civilization.
They know that they can't simply build out the boiling water reactor, since it was designed for enriched uranium and light water as a moderator, and enriched uranium is well beyond the capabilities of what's left of human civilization.
However, they have access to large amounts natural uranium, perhaps because it's renowned as a very hard and dense metal that makes glass glow a pleasing shade of green. Let's also assume that they have a source of relatively pure graphite, and cadmium, which is renowned for its ability to create yellow pigments. The toxicity of uranium and cadmium as heavy metals is a moot point, as the harsh conditions of the apocalypse has forced the evolution of an extremely high tolerance for them, along with the radiation that a nuclear core would emit.
The mutants are able to gather enough of the raw materials, and their craftsmen are able to build uranium rods and flat cadmium plates. They also purchase large blocks of pure graphite and drill holes through the center of them while also cutting them into perfect cubes.
Inside the abandoned reactor pressure vessel, they stack the graphite blocks into a much larger block, leaving grooves between some sides of the blocks. Between some of the graphite blocks they slide the cadmium "control plates" into place to prevent the reactor from going critical. Lastly they slide the uranium rods into the channels they cut into some of the graphite. The rods are designed to be slightly narrower than the channels in the graphite blocks, and thus allow cooling water to flow around them.
They flood their contraption in the reactor pressure vessel and tie chains to the control plates.
The reactor vessel's cap is lowered into place from above using pulleys and levers, as well as manpower from the strongest mutants in the group.
Ahead of time, they had the forethought to cut a small window in the side of the reactor pressure vessel. The window is made from sapphire glass they found at an abandoned laboratory and is capable of handling extremely high heat and pressures, but they won't have to worry about pressure too much in their reactor design.
Very carefully, and extremely slowly, they withdraw some of the cadmium plates. One of them peers into the reactor through the window and notices a faint blue glow in the water below. This Cherenkov radiation is an indicator that they have successfully achieved criticality. The water acts as a fine shield at lower powers, but even at high power the mutants' great resistance to radiation means that they will be fine with people in close proximity to the operating reactor.
They then slowly draw the control plates further, carefully monitoring the brightness of the blue glow of the reactor. Soon the water begins to churn and heats into steam, and the steam system of the plant pressurizes. The turbines roar to life as they consume the steam. Your mutants have managed to make the plant generate electricity.
However, 150 years is a long time, and nuclear power plants are extremely complex machines. Without proper lubrication, the turbines are unable to spin at full power, and the relatively crude reactor design is not very efficient at generating steam.
The plant is unable to generate anywhere near its original 1 gigawatt-electricity design, but it doesn't matter. There isn't enough civilization to consume that much energy anyway. Your mutants are satisfied with a few hundred megawatts of electricity, and the fact that the plant works at all is a marvel of the region and causes the mutant settlement to grow rapidly. A new city is formed around the abandoned plant.