Thanks for reporting this, it's helpful. I found the issue, and we'll fix it. We incidentally created a second account for you based on your SO activity when we migrated to Careers 2.0, in addition to migrating your old account (rather than just keeping your old account). This new account is now linked to your SO account and so when you go to careers that's how you'd be logged in automatically. It's also the account the invite is now associated with. We did detect the other account, and the request to log out and back in was so we could authenticate your old account and theoretically merge the two, but this clearly did not work as intended.
I'll email you once we've merged the two accounts.
In general, this issue affects a small number of users, so if anyone runs into any problems, email [email protected] and we'll sort you out.