Authoritarians are invariably toxic damaged people who are full of rage and are looking for a target to make themselves feel better.
Sometimes they end up on the left. Sometimes they end up on the right. Sometimes they end up in management or venture capital.
Same issues, same dynamic, different context.
The difference is authoritarians on the right are more likely to use physical violence. "Cultural" authoritarians are more likely to use social exclusion - brigading on social media, getting people fired, and so on.
The key point is that the presenting issue is irrelevant. The social dynamic and mode of relationship - angry tribalism used to justify violence without any sense of context - is the real tell.