@Astrid: try to login as an existing user which has not yet answered the privacy policy. Trying to save (or to cancel), system hangs, I can only logout via backend and throwing out.

I am having absolutely no issues with this.

Warning
The email address you entered is already in use. Please enter another email address.

That would not be caused by core CB. CB does not have any control over Joomlas user store behavior. The only issue CB can cause here is an infinite redirect loop where save does absolutely nothing, which we've already fixed.

Logging in as existing user who has just accepted the privacy policy has no problems. New user have no problems.

This is likely because you've a storage problem with existing users. Probably from a 3rd party extension or Joomla event usage in a CB plugin.

Testing with only community builder system plugin disabled: problem persists. Only when uninstalling community builder, problem is solved!

If the problem persists after unpublishing CBs system plugin it can not possibly be core CB. It is possible you've installed a CB plugin that is acting on a Joomla event. Are you using CB Auto Actions to act on a Joomla event for example?

@Astrid: thanks. I tested on an other fresh site and it worked. There seems to be a problem on one of my main sites. What shall I do: Uninstall and reinstall all cb?

Review what you've installed and begin unpublishing 1 by 1 until issue resolves. This will give you the culprit. It however sounds like it's a CB plugin acting on a Joomla doing it, which is likely a auto action in CB Auto Actions is my best guess.