Thank you for the picture. That helped narrow things down. There are a few reasons you had that, and other issues, on your site:
MySql connection error
This was happening because you had the Custom DB profile plugin enabled but had not configured the database settings properly. That plugin lets you store user profile information into a separate database table. The information you had for database, username and password were not correct, so the error was showing and preventing registration.
I disabled this plugin and the registration error went away.
Joomla Profile plugin was enabled
The Social Profiles - Joomla plugin is meant to import user information into the User - Profile plugin that comes with Joomla. The User - Profile plugin is disabled, so there is no readon to enable the Social Profiles - Joomla plugin. This wasn't
Automatic registration isn't working
Automatic registration will fail if the user logging in through Facebook or Google doesn't have the same email address of an existing Joomla account. If there is already an account on your site with the same email address, JFBConnect will redirect the user to the form-based registration page to enter a new email address.
There is a setting, "Automatically Link Users by Email". If enabled, then the user logging in will automatically be 'connected' to the existing Joomla account. It sounds like you want to enable this setting.
Joomla system messages are not showing in the front end
Your template is not properly showing Joomla system messages (notices, warnings, errors) on the front-end. That's hiding a lot of messages that JFBConnect would show to let the user know that their email is already used or that automatic registration is failing. I'd recommend contacting your template developer and having them add the Joomla System message output to your template.
I hope that helps,
Alex
registration PROBLEM
