I run a few other sites with Rocketheme templates that (of course) use JFBConnect. I haven't seen the issue you mention and I just tested to double check. The site below is using the Gantry 5.4.31 plugin (slightly out of date).
I just checked the Menu selection and Assignments (when in a style) areas. They look normal to me and nothing changes whether the JFBCSystem plugin is enabled or not.
Can you try re-ordering the JFBCSystem and/or Gantry plugins so they go before or after the other? Something is obviously different, but unsure what from a quick investigation. We'll gladly help narrow things down however we can though.
Thanks,
Alex