I just tried to login using LinkedIn and I was brought back to the following URL:
/index.php/component/community/register
That page was a blank white page and hitting refresh didn't work for me. My guess is that registration isn't working at all, but logging in partially works where you can hit 'refresh' to fix the glitch. Obviously, neither is correct.
What I'd recommend to narrow things down is:
1) Go to the Joomla -> Global Configuration area and set "Error Reporting" to 'maximum'. That should display a PHP error message on the blank white page and that will help explain what's going wrong.
2) If you have the "JomSocial Redirect" plugin enabled, disable it. That's caused some strange issues in the past and may fix the problem if disabled.
3) Disable any socialprofiles plugins you have enabled and test if the issue goes away. If so, re-enable the socicalprofile plugins one at a time (if you have multiple enabled) and see which specific one is causing the problem.
I hope something above helps get you going, but if you still have issues, just let us know. We'll gladly help investigate further.
Thanks,
Alex