Disable parts of the BuddyPress Social navigation bars

I would like to disable the "Visit" drop down in the top navigation bar, and the entire second navigation bar (Home, Activity, Community, About, plus any other tabs in this navigation bar that might appear) for non-logged-in members. I would like these features to be restored once a member logs in. How would I do this? Would it be best to add navigation.php to the Child Theme, so future upgrades do not destroy the customization?