That is more because Mando order didn't allow him to remove in front of others, Boba don't have that problem.
Maybe they put Bob showing off his face more as a counterpart dynamic of Mando not showing at all(its his "uniqueness"), Because outside battle, he doesn't need the helmet.
It also could implies that he wanting to connect with the other crime bosses, something with the helmet would make things difficult, as it may show suspicious dealing with someone who cover his face.