I have found on Stack Exchange exactly the same question. All my attempts to subscribe to Google Groups without entering my Gmail account simply fail. When I send an email to beaglebone+subscribe@googlegroups.com, I correctly get the invitation mail, where I have to click a link to verify the address.
When I click this link, it opens a Google Groups page, but it asks me either to create a Google Account, or to log in. There is no other option.
Is here anyone who has succeeded to subscribe to a group avoiding any interaction with Google Accounts? I guess the former page recipes do no not work because they are outdated.
Best Answer
Don't click the link in the email--REPLY to the invitation email. Don't type anything, just Reply and Send. You should get a confirmation email that you joined.
I am running a Google Group where this works because of certain settings I chose; the Group you're attempting to join may require Google accounts, in which case you're out of luck unless you can get them to change.