I have developed various types of login integration for both vBulletin 3, 4 & 5, for example like Google, Twitter, Facebook, Steam, Discord, GitHub, which works both for registration & login. While 3 & 4 versions are fully working, versions for 5 needs improving since the current vB 5 is still not ideal for external plugins. Depends on your request, I can quickly setup a board with the plugin for you to check, since it's already made.
The bid is for one site. Let me know if you need any other information.
Thank you.