It's redirecting you to registration after being logged in or it's sending you to registration with a prefilled form? If it's just trying to redirect you to registration after login then you can specify a login redirect within CB Connect. That however is a known issue to be fixed as it shouldn't try redirecting to login page or registration page, but currently does if it was the previous page the user was on.

CB Connect works perfectly fine in all my tests. Once registered using CB Connect their account should have Facebook ID field populated with their Facebook ID. You can verify this by editing them within CB > User Management. If it's not populated then you've something breaking CBs registration process of CB Connects registration process. It's usually something configured to act after registration causing a user store resulting in the Facebook ID not storing. It is the sole factor for linking the two accounts. If it's empty it will not be able to log them into that account.

I'm out of ideas. CB Connect works fine in all my tests. Please PM backend super administrator login credentials and will review your configuration.

Have reviewed your install and CB Connect worked perfectly fine for me. Your cb_wojewodztwo2 field was causing registration to never complete. I did not dig into it deeper, but it wasn't available during registration yet is marked required throwing a validation error that's impossible to complete. I've unpublished it to resolve this. Once successfully registered I confirmed the user then used the Facebook button on your login page again, which promptly logged me in. Your login redirect URLs were also invalid and I've corrected them, which maybe what was causing your issue. Please give it a try now and see if it works fine for you.