Not quite. It's about ideological alignment and purity. The cancel mob just got Antonio García Martínez fired, for example. And they are constantly trying to cancel Glenn Greenwald, a gay man married to a minority POC, and with minority kids.
I don't know Antonio García Martínez's ethnicity, but he looks and sounds very much like a straight white male, so I would not consider that a counterexample. Also, certainly there are no absolute laws of who is always targeted and who is never, just clear trends.
However, it is true that to some small degree I am oversimplifying something quite complex, partially because the cited example was James D'Amore. Other examples you might cite include Dave Rubin or Ric Grennell. Certainly gay white men and straight white women (specifically if they are Republican) are targeted. What happened at Disney with the treatment of Gina Carano vs. Krystina Arielle is evidence enough of that.