I grew up in an impacted area; you might call it downwind of Chernobyl. My mother had thyroid cancer at a young age and now had no thyroid. Numerous female relatives as well as friends and acquaintances have experienced similar problems and those are all associated with Chernobyl.
Here’s a single scientific source. There are more, but I’m sure you’re eager to demonstrate your hypothesis that women in Eastern Europe are getting cancer not from industrial accidents but from cousin marriage.
My mum died when she was 36 because she had spent a couple of years working in a battery production factory in LT. I remember visiting her too! The amount of cancer, the locations of it and the aggressiveness of the growths found in her pointed to the simple fact that she was exposed to incredibly harsh chemicals. But it could be blamed on X, Y, Z if need be but this is the reality of it.
Cousin marriages and cancer? Wow.
Thyroid issues are super common. Might be related but also may very well not be.
(I’m not taking a position either way as I have no data, but they’re clearly not accusing Chernobyl neighbors of mating with cousins.)
Even then there will be confounding effects. People are, generally, richer now than pre-Chernobyl. They will, generally, have better access to better healthcare.