You are correct that it wouldn't be formal. You are WAY OFF in thinking that informal isn't just as, if not more important.
Specifically, you're missing how then, e.g. white conservative majority power didn't need formality to suppress. That's how majority power works. It can just good-ol-boy network its way to suppression. (And note how it doesn't need to be precise when it's like that. It doesn't have to "make an argument," it can, e.g. just deny tenure to the loud black lady on some random grounds.)
Formality is usually what the WEAKER side must resort to. Now I think there's a reasonable argument that that process is much stronger in a negative way today -- but context.
The suppression today involves professionally disasterous public things like firings, censures, formal censorship, pressure to sign petitions, reputational destruction, doxing, physically threatening pressure and screaming and possibly violence, etc. If only it were eye rolls.