I have set up a free event (type "webinar") with online registration, but Civi automatically rejects anyone registering for the event. It is not related to waitlisting because the behaviour continues when I disable the relevant status categories. Can anyone help?
Welcome to CiviCRM SE. Could you please provide some more details about 'rejects anyone registering for the event'?
If users are getting errors on the screen please can you add the error message to your question?
Check in CiviCRM config log to find if any error was recorded during user registration.
Check if the problem is specific to a single event or any event.
In case your system has a module/extension/plugin related to the Event, turn it off and check if the problem resolves.
If you have Civi-rules for Event, turn it off and check if the problem resolves.