I have the same issue.
I created this account using Tor and only sign into it through the Tor network, which means that it is a fairly anonymous email account. Tor does store cookies, it just deletes them at the end of the session and doesn't mix them with non-tor cookies. I have been using this account for over a year, and I do not believe Tor and Gmail to be mutually exclusive -- a few years ago, Gmail was known for being as open to internet security practices as services that feature that, like riseup.net
I'm wondering if someone from Google can comment on whether this change to lock out Tor users is deliberate or not. If it's deliberate, that's fine, I can understand that Tor use messes with their information collection, which is one of the reasons why this service is free. I will simply switch to a different mail service, but I don't want to do this if the problem is an inadvertent one that Google might fix.
I haven't been able to access my account for several days now, and will wait another couple of days before switching. If anyone can shed a little light on this issue, or offer another workaround (I'd been doing the same things that above described), that would be wonderful. If not, then see you on riseup