If I’m an American citizen born in USA. My parents where born in Romania can I get a EU passport? What’s the downsides
Are you saying you can get a Romanian passport, or asking if you can? If the latter I don’t know the answer.
I know that Hungary has some laws for citizenship for those with Hungarian heritage, but it varies by which parent had citizenship (mother or father and/or whether they were born before or after 1957. If it’s a grandparent then even if you can prove it you’d have to learn Hungarian, which is not an easy language to learn.
There was also some discussion on DDF recently about German and Austrian citizenship for descendants of victims of nazi persecution.
It’s possible Romania has something similar, but I’m not sure. If you do find out anything conclusive please post back with more info.