When they get Not Authorized are they sent to the Category of the group or are they sent to Overview? Check the Access for your Group and the Category of that Group to ensure the user can even access them. Invites will not bypass Access restrictions.
I also get "Error loading component: index.php?option=com_comprofiler, 1" for those users as they login for the first time.
On first time login only? Check first time login redirect within CB > Configuration > Registration and ensure it's valid.