BuddyPress.org

There are bunch of ways to make this happen but here is what I use.

https://wordpress.org/extend/plugins/bp-registration-options/

Oddly enough imo the plugin authors don’t really showcase the privacy feautre which I think is one of the plugins best quallities.

Here a creen shot of the privacy settings page is it appers on my install.

http://preview.tinyurl.com/4gybrxp

very bassic but it really does the trick if you are trying to limit access to member profile pages.

Hope this helps!