I found it.

It was a plugin called "Block disposable addresses" which is supposed to block certain email addresses from being registered.

The reason why it worked in my local copy is because I haven't got a firewall while the hoster's firewall is on. This plugin obviously wants to "call back" to check the addresses. The new installation I had set up for testing purposes didn't have this plugin installed.

It obvioulsy doesn't work with the Joomla! standard logon module either, because the registration only took a second when CB was deactivated and the standard module used. It only seems to "call back" and check the mail addresses with CB. That was what falsely let me to suggest that CB might be the culprit.

Anyway, in case someone has a similar problem, I hope this thread can help solve your issue too.

And thanks a lot again for the fantastic tool CB!