We are happy to announce that the broken Google logins to Studio are now fixed!
In short, it was a bug in Google's OpenID service. After entering your credentials, Google sends us an unique OpenID URL that Studio uses to identify you and associate your Google and Studio accounts. However on August 9, Google started sending different URLs, so Studio couldn't match it to your existing account and presented a new one instead.
We initially suspected it was a bug on our side (eg. we recently upgraded to Ruby 1.9, among other things). But after inspecting all recent Studio code and configuration changes, as well as communication logs, we still didn't find anything wrong. Eventually we were convinced it was a Google bug and reported the issue. To our pleasant surprise, Google responded and pushed a fix within 48 hours.
Signing in via Google should work just fine now. If it doesn't, let us know in our forum (linked to a mailing list) so we can investigate. Please include your Google account name and display name in Studio. You can also use the Send feedback link within Studio once you're signed in, to report issues privately.
What we learned
When working on this issue we noticed a few sub-optimal things within our code and infrastructure. For example, we don't keep logs of the OpenID communications with the various providers. We will implement measures to help us detect and resolve such problems more quickly in future.