BuddyPress.org

“If I activate it and set a field (e.g. birthdate) to “users only” – nothing happens. There are also no settings for the users in the frontend of buddypress.”

If you set it to “users only” in Admin, you’re not giving your user the choice, and that’s why there is no selector in the front end. The user will only get the selector if you choose “let user decide”.