It doesn't if you build them away from cities, which many countries are capable of doing.
The biggest problem are the shrooms because they actively seek out and concentrate radioactive elements in the ground for whatever reason, and then the wildlife eats the contaminated shrooms, further concentrating the radioactivity.
[1] https://www.jagd-bayern.de/jagd-wild-wald/jagdpraxis/rcm-mes...
[2] https://www.merkur.de/bayern/bayern-wildschweine-tschernobyl...