I have fields and tabs published for display on the registration form. The registration form worked just fine in CB 1.1. I have also unpublished the tabs for all third party CB modules.
And as I said before, my Check Users Database comes out green.
Should I try uninstalling CB 1.2 and reinstalling?
Yay! Thanks for figuring this out! Apparently this was my problem too. It must be a setting that's somehow set by upgrading from 1.1 to 1.2 because I definitely didn't set it to that manually.