Are you using any WordPress user/member plugins to control access to different sections of your site?
Things also look weird with the theme you are using, what happens if you you switch back to Twenty Eleven, Twenty Twelve themes shipped with WordPress? Do you still see the same issue?
It may also be a plugin conflict
To try and resolve conflicts with other plugins please disable all your plugins except bbPress to see if the error persists. Re-enable each plugin one at a time and if things break again you should be able to now know which other plugin is causing the conflict.
I deactivated all plugins except bbpress, then one by one activated them. After I had activated all of them, my forums miraculously decided to work again! Thanks so much though Stephen 🙂
I had this same problem on a site in my Multisite network (the only site with bbpress activated). I fixed it by checking the “Auto role: Automatically assign default role to new, registered users upon visiting the site” option in Settings –> Forums. The default role was set to “Participant.”