I think I fixed it by checking the reset box after changing the header path.
Edit: No, not fixed. It works as it should with the default XF logo in the header but I add a custom logo it requires a password to enter the forum.
ReEdit: And now it is working like it should. Very weird. Is there some kind of timer for header edits?
This is typically an issue with using www or not using www in the URL. You need to force one or the other and make sure all links in the Basic Options are set accordingly.