1) Foxes are, in fact, not immune to radiation. Radiation causes cancer in literally all living things. In fact, Foxes are of the order Carnivora, which, according to a Nature article written by 12 different scientists (https://www.nature.com/articles/s41586-021-04224-5), has a HIGHER cancer risk than all other mammals. Not only that, but carnivores are more likely to die of cancer than herbivores.
2) Radiation fizzles out over time. Using Chernobyl as an example, the radiation amount there is now around 1.6 microsieverts, whereas the background radiation in somewhere like Vienna is 1 microsievert. This is tiny compared to the 31 microsieverts recorded after the explosion, which is huge.
3) In fact, of the 134 who got exposed to high amounts of radiation, 28 died within 3 months of the disaster, which means that there was a mortality rate of nearly 21%. Considering that the normal mortality rate for primates like humans is 5%, this means that the carnivore 10% would be scaled up to 42%. So it's likely any foxes that WERE around Pripyat at the time of disaster died off relatively quickly.
4) Because it was a nuclear facility, they probably didn't want anything to mess it up. The reason there might not be foxes around ANYWAY is because foxes, like other wild animals, could cause damage to the plant that couldn't be fixed in time. Similar reason to why a lot of power plants today have barbed wire.
5) The land was originally nature's. People built something on it, it blew up, the people left. Humans don't want to go back to Chernobyl, which means there is nothing in the way of foxes proliferating around the reactor. Just because there was a shit-ton of radiation there in the 80's and there's thousands of foxes there in 2022 doesn't mean foxes desire nuclear disasters.