Hi.
Related to this issue (https://wplms.io/support/forums/topic/bp-social-connect-issue/). When the user finally is created and the redirect occurs to the home page (although i've set to go to the course page). But the real "issue" is that, the cache of the homepage (no plugin for this) prevents the user to see that he is logged. Because the top menu keeps with the login/register instead of the name and picture.
Ideally when a user logs in then your server should clear your cache.
Are you using any plugin for cache, we do not recommend page caching plugin for WPLMS. You can also disable caching for logged in users as well from your plugin options.