How radical are we talking? I might have an issue with "eliminating all men" radical, but I'm good with "Michelangelo is a party dude" kind of radical.
As a seperate top-level answer: no, would not pursue a romantic relationship with a woman who repeats sexist assertions about men. Because i am both a man and a feminist, and my several decades of happy married life have taught me that compatability of strongly held beliefs is a key to romantic happiness.
I would also not encourage the young men and women i know to either espouse sexist positoons or pursue potential partners who hold such beliefs. And i would probably also ramble for a bit about how all labels are imperfect and you should not necessarily dismiss someone just becsuse of a label.
If you want to date someone who describes themselves as a "radical feminist", a date might be a good way to discern if they are an "all men are evil" feminist or a "men are awesome and also victims of the patriarchy" feminist.
A hardcore feminist who goes to every rally and protest, donates money to things like planned parenthood and so on. - probably a cool person, but might have their head up their ass. However, their heart is probably in the right place regardless of their personality.
A misandrist. Fake feminist who hates men and believes men are the source of the world's problems. - almost certainly an asshole and should be avoided.
A terf, aka "trans-exclusionary radical feminist". Also a fake feminist. They don't believe trans women are women and seek to exclude them. - asshole, avoid at all costs; tend to call themselves "gender critical" because the real feminists got tired of their bullshit and started kicking them out.