Rasmus,
I just registered on your site using Firefox 12.0. The process went smoothly and expected for me.
Can you let me know what happens when you try to login? Do you get an error? Does the page not reload? Any information you can provide about what is or isn't happening, and what's different from IE, will greatly help.
Finally, if you were using a previous version of JFBConnect on the site, simply try clearing your browser cache, as that may help clear some things up as well.
Thanks,
Alex