Is this the "anti-semitism" to which you refer?

Quote: Communism promised to be both morally and economically superior to capitalism, but every attempt became morally corrupt and an economic failure. As it became clear that the working class of the liberal democracies wasn’t going to overthrow their “capitalist oppressors,” the Marxist intellectuals transitioned from class warfare to gender and race politics. The core oppressor-oppressed dynamics remained, but now the oppressor is the “white, straight, cis-gendered patriarchy.”

Yes, parroting debunked anti-Semitic conspiracy theories is anti-Semitic.

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?