@chris thank you very much!
This raises a new question:
I've hidden the "Members" tab from all the members because I'm using Memberpress.
Wpforo assumes everyone - even non-paying subscribers - is a member.
So I'm blocking the access to the forum through rules inside Memberpress and not through User Roles.
How can forum members find out the nicknames of other members without getting access to the "Members" tab?
wpForo users system is based on the WordPress user system. All forum users are the same WordPress users. There is no forum specific user in WP/wpForo website. When you log in or register in the WordPress, you automatically log in or register in the forum too.
Please go to Dashboard > Forums > Usergroups and check the usergroups "CAN's" for example you can see there an option like "Front - Can view members" or "Front - Can view profiles".
Also check Forum Accesses(CAN's) from Dashboard > Forums > Settings > Forums Accesses Tab, for example "Can view forum" or "Can enter forum".