All IPB, vBulletin, phpBB forums have a registration option, there is an option to restrict posting only to registered users, restrict viewing only to registered users, and even enable pre-moderation of publications in separate sections... And there you can flexibly set up distinctions by group, sections and features .
If you need a free product, then phpBB
If you have some money, then vBulletin or IPB is already a taste and color. In terms of functionality, they always go head to head and it's only a matter of habits and love. For example, I always liked a roll more, although I spent a lot of time with IPB.