Error 500 linkedin login

Not sure, off hand. Can you try the following and let us know if it helps narrow anything down:
1) Disable any JLinked Profile Plugins you have enabled.
2) Turn off any SEF extensions you may have enabled (temporarily at least).
3) In the Global Configuration area of Joomla set "Error Reporting" to "Maximum" and turn off GZip compression.
With these settings, when you try to login, hopefully, you will see a more explicit error of what the problem is.

Test at each step, just in case that's the step causing the issue. Let us know what you find. Additionally, feel free to private message me the URL of your site and I can take a look at the front end to see if there's any obvious issues I can see. You can PM me by clicking the arrow under my picture (<----) and hitting the mail icon.

Thanks,
Alex