So if someone who is anti-semitic believes that Jesus died on the cross at the behest of his Jewish contemporaries, and I also believe the same thing because that's what history has taught me, does that make me anti-semitic?

Or is that one ok because it hasn't been debunked?

In which case, according to Wikipedia, the Frankfurt school "consisted of neo-Marxist dissidents uncomfortable with existing capitalist, fascist, or communist systems." Has that been debunked? If so, where?