Currently, there is no way for an SO admin to control what an SO user is able to add through their Profile page.
In Portal, the user.form.my.account properties can be set to allow control for what a user can and cannot add through My Account. However, this does not affect Profile in any way and has been reported as a bug in SOS-2411.
Currently, an SO user is able to control what can and cannot be visible on their SO profile through the portlet configuration. But this can only be done for their own Profile, not anyone else's.
Thus, there should also be a way through the SO GUI (possibly through the Profile's portlet configuration) that allows an SO admin to control what information can and cannot be modified and viewed on the SO profile for all SO users.