• Use a custom menu with only the links you want.

• Remove Profile, My Posts, etc. using:

add_filter('wpforo_menu_user_items', function($items){
unset($items);
return $items;
});

place this in your functions.php

Please read this support topic: https://wpforo.com/community/how-to-and-troubleshooting-2/how-to-hide-the-entire-forum-behind-a-login-page/

The same issue is discussed there.

However I notice that I can still open the forum even if I'm not logged on. I'd like it to be more private. Is there a way to make my forum non-viewable to non-members? 

Are you sure you're checking as a regular user? Probably you're checking as admin of your website. 

The option I mentioned removes the 'Members' menu items from the navigation section. In other words, if a user doesn’t have the 'Can View Members' and 'Can View Profiles' permissions, those menu items will not be visible to them.

I've taken the steps you recommended, however the "members option" is still on the menu in each of my forums. See screen shot - I've unchecked the two options but the menu is still viewable along with all members. Even as an admin, I unchecked the two options, but the menu option is still there along with all the members.

Is there another step or something I'm missing?

The option I mentioned removes the 'Members' menu items from the navigation section. In other words, if a user doesn’t have the 'Can View Members' and 'Can View Profiles' permissions, those menu items will not be visible to them.

Ideally I'd want to keep the member view if I could restrict it to members of the membership that has access to the forum. I don't want members of forum x to see the members of forum y - both of whom are in different memberships.

I'm sorry, but the wpForo doesn't have such an option. 

I guess I wasn't clear. Is there a way to entirely remove the "members" link in the menu bar itself? I don't even want that to be an option. I've checked out your links and haven't found any info for that.

If this is not possible, then my second question still remains which I also haven't found an answer to:

Ideally I'd want to keep the member view if I could restrict it to members of the membership that has access to the forum. I don't want members of forum x to see the members of forum y - both of whom are in different memberships.

I'd like to remove the member view while keeping the menu bar available. Basically take "member view" off of the menu. Is that possible?

Please navigate to Dashboard > wpForo > Usergroups, then edit each usergroup one by one and uncheck the "Can View Members" and "Can View Profiles" permissions.

I also recommend checking out this FAQ: https://wpforo.com/community/faq/wordpress-user-roles-wpforo-usergroups-and-forum-accesses/#post-39664

It will help you better understand how wpForo Usergroups, Forum Accesses, and WordPress User Roles work together.