Peter,
That's not an issue we'll be able to look into soon. We've never heard of that plugin and can't imagine why it would be blocking our profile import. If it's hijacking the normal registration/login flow in a way that is not normal for Joomla, that's definitely bad and the cause. There are hundreds of other user plugins that JFBConnect works just fine with, so I'd recommend contacting the developer directly to see if they can understand the issue more or explain what they're doing to auto-log the user in.
Hope that helps get you started,
Alex