This has nothing to do with cookies or the problem concerning cookies as far as I know.
That being said, after I downloaded the new Pokemon update today (7/31/16) after opening the app, it prompted me to login.
I proceeded to login with my Google account. After I type in my email and password I click "allow" giving Pokemon GO permission to access my email and other things. After I click "allow" I get redirected to the Google homepage. From here, I cannot do anything except hit the "done" button.
After clicking done it prompts me to login. Over and over and over again. This has been going on all day and have not been able to find a solution.