Hi, Andrew.
For profiles in your Family Group born within the last 150 years, you're allowed to make those private, but you have to do it manually on each profile, the way you've been doing it. Keep in mind, however, that other users in the Family Group for those profiles can choose to reset them to public again at any time.
The goal of Geni is to have one shared family tree, so private profiles are generally discouraged.
