FBC nor CB Connect use CB Login module or CB configuration redirects. Next release of FBC will have parameters to configure registration and login redirects. Current release of CB Connect already allows specifying redirects in CB Connect configuration. There are some known issues with FBC not allowing properly login currently due to some API changes on Facebooks end. Next release will also be addressing those issues. We're looking to release FBC 1.4 sometime this week. You could also opt to use CB Connect instead, which already has the fixes.

FBC 1.4 has just released. Please download and confirm if you're still having issues. You can now also specify login/registration redirect URLs in the parameters. Have fixed many internal bugs which should address most if not all issues.

I have removed the FB component and it works fine.

How does removing FB cause FB to work fine? Am confused, did you have multiple FB extensions installed? FBC 1.4 is tested working perfectly fine. If clicking the button does nothing then you've a fatal JS error present on your page somewhere preventing FB JS from working. FBC 1.4 features redirect on registration/login parameters now as well so it's possible to redirect FB users.