WordPress custom login and register page problem?

One way to make the Log In page your landing page is to go to Dashboard > Settings > Reading and find:

Front Page displays ( ) Your latest posts
(x) A static page

Select your “home page” (which will be the Log In page) and your blog page appropriately in the drop down menus.

Regarding buddypress tab/menu structure… I’m not that familiar with that. I feel like there’s some code you can just add to your child theme’s functions.php to remove that sort of feature but I’m unsure what.