Some are and some are not... Most of the Chernobyl exclusion zone now has less radiation than natural radiation occurring in the Black Forest. Many species thrive; with comparable life spans and no significant anomalies, these are especially larger multi-celled organisms. Some organisms that have few anti-oxidants; especially some annual flowers and Bactria don't fare quite so well.
You must take into account tow issues, first the high radiation environment killed many organisms; especially single celled organisms. This has caused oddities, such as the Red Forest, where almost not decay is happening, because the bacteria and small organisms where all killed off by the radiation. This is still the case, because it takes time for Bacteria and small organisms to repopulate the area. (And they are still partially dying of mild radiation.) The second issue is, that because the the amount of anti-oxidants in the organism determines if it will thrive or not in mild radiation. it has brought the ecosystem somewhat out of kilter. Some ecological niches are not or only badly accounted for and this creates the situation that some organisms could survive the mild radiation, but can't because their dependent niches are empty.