If the argument that being antisemitic precludes you from being a leftist, that’s not a fallacy. If you don’t abide by a set of beliefs, then you are not a follower of those beliefs.

I’m not a Scotsman because I’m not from Scotland.

Similarly, I don’t think most libertarians are true libertarians because they don’t care about liberties except their own. And if that’s the definition of libertarian, then everyone is a libertarian.