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.
WORKING SOLUTION:
You want to go to Settings, Content, Cookies, and instead of a destructive clearing, you want to Allow:
GoTo opera://settings/content/cookies?search=Content+settings
OR
opera://settings/content?search=Content+settings
(then find Cookies)
OR
Goto opera://settings
(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.
