Jews(at least some) dislike people that are not from a "pure" jewish lineage, if your father or or grandpa was not Jew, then you'll suffer prejudice. Must be worse with converted people.
So want to join the Jews without a pure jewish lineage wouldn't be too diferent than want to join the nazi party without pure arian lineage.
I believe it's through women not men (perfectly logical BTW, as there is no way to get it wrong, unlike with men who couldn't in the past ever be certain they were actually the father of their children).
Since a couple of months ago I have a Jewish niece by that definition. Her mother isn't practicing though, and my brother didn't convert nor cut off part of his dick or anything like that !