So I have it working with LinkedIn only and it seems to be working ok - took out all Login form input on the login/registration page, and kept only the LinkedIn connection because I want to force all users to create accounts using their linkedIn accounts, and not give them the option to create them directly via WP.
All seems to be working pretty well, but the page that the user is supposed to be redirected to when they first login is not changing no matter what I put in that input box in the admin backend area, it just always redirects to site_url/login. It's as if in the admin area, the call for the "Home Page" ie, SocialAuth_WP_user_home_page is broken.
Also, the avatar is pulling the default WP avatar, not the LinkedIn one.
I do also have Buddypress installed, but I don't think that's the culprit.