Uwe,
No worries. Sorry for the delayed response. It was an easy fix that we wish we would have provided when you asked originally.
I just logged in, and then logged out on your page and didn't see a permissions error. When you see it, is it a Joomla error saying that you're trying to access protected (registered only) content, a Facebook error, or something else? If it's a Joomla error, try setting a logout user redirection. If you don't have this set, we'll try to leave the user on the same page that they logged out from.. however, if that's normally a registered page, you'll get the Joomla "Require Login" page.
One final note, I noticed if I go to your page without www and try to login, I get a Facebook error. This is usually caused in your Facebook application settings. Make sure the following settings are configured like below:
Site URL:
www.blink-182.de/
Base (or Domain) URL: blink-182.de
Mainly, you don't want www in the Base/Domain URL. That will let the Facebook application work on www or non-www pages.
Hope this helps!