You said: "He has successfully sued people for claiming he is a Nazi, white supremacist and other things." 

No, he didn't.

The NYT changed the headline and left the article unchanged and he, apparently, gave up the lawsuit. 

Your "very simple fact checking" about the initiation seems to rely on taking McInnes' unverified word.  The NYT got its information from a Proud Boys member, who described the ritual as a time to “announce yourself as a white, proud Western chauvinist, make sure everyone knows it, and don’t be ashamed."

I'd say that statement shouts "white supremacist."  You say: "He is not going to sue them for their characterization of it. Why would he?"