As it happens Google's own Chrome was hit this same way. Not every user seems to have the problem - Opera, Chrome, and all Chromium based browsers run into this. But not all of their users experience it. Sadly, Google, Opera, etc., have responded poorly to this bug.
You want to go to Settings, Content, Cookies, and instead of a destructive clearing, you want to Allow:
(then find Cookies)
(then look for Content Settings, then Cookies)
Clicky triangle to open Cookies panel.
Under the Allow section, select ADD.
Refer to the tab where you got your original ERR_TOO_MANY_REDIRECTS error.
You'll see a URL just below the error. That's what you plug into the Cookies-Allow section.
We should not have to fudge around like this, but, blame the Chromium makers and Google:
In the case of our GMail problem you want to Allow mail.google.com
Or if it's an accounts problem, then allow accounts.google.com
You get the idea.