But as it turns out by checking with a few Regular user's permissions, every user can see the added custom profile fields.
This option is selected and active;
Checked all kinds of permissions, but I can't see why 'everyone' can still see the custom profile fields?Hide profile field:
Hide the profile field from all other users except the user, administrators and moderators who are still able to see this field. If the Display in user control panel option is disabled, the user will not be able to see or change this field and the field can only be changed by administrators.