Okay, thanks to Burt for waking me up enough in IRC to point out my errors, here’s what you need to place in your bp-custom.php file:
remove_filter( 'bp_get_the_profile_field_value', 'xprofile_filter_link_profile_data', 2 );
add_action( 'plugins_loaded', 'remove_links' );
That should work.
I’m going to get some sleep now.