Thank you very much, Jeremy!😀  I did this now and it works great. Except that in person's profiles still some sensitive information is visible: the name, the cover image and the profile image of the person. Did I miss something? Can I hide these too?

I think that the easiest way to not show profiles publicly using permissions.  Go to Studio > Permissions > Actions > select "Unauthenticated" > turn off "View Person's Profile" action