I'd like to offer a counterexample to your thesis.

Medium writer Argumentative Penguin is both someone who has argued against cancel culture (see here: https://medium.com/lucid-nightmare/is-cancel-culture-the-new-boycott-4843e7d2defe), and someone who has demonstrably fought against bigotry in their community (see here: https://medium.com/lucid-nightmare/oh-penguin-where-art-thou-8e182dd47ff6).

This is an example of why your thesis is a bad one. It encourages making inaccurate assumptions about people, and ultimately just provides people with a very lazy excuse for being prejudiced against people who aren't already of the same opinion as them.