There's definitely a lot of users that use the T3 framework and JFBConnect without issue. I haven't heard of the ThemeMagic issue you posted about, so it seems more specific to your site for some reason.
My best recommendation is trying to disable the "Include jQuery / Bootstrap" setting in JFBConnect to see if that fixes the issue. Of course, make sure that all JFBConnect features continue to work as expected then too. That's the only Javascript that really could cause any conflicts. If that doesn't help though, please let me know.
Thanks,
Alex