> This idea seems to be popular at the moment, but I can't find any proper backing for this claim - that one is disproportionately worse than its counter-parts - other than repetition.

I don't know if the left is any more guilty of orthodoxy, but as the left currently dominates academia, we can see more examples of the left enforcing orthodoxy in academic settings. For example, FIRE tracks campus disinvitations from both the right and the left, but the vast majority come from the left: https://www.thefire.org/resources/disinvitation-database/