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
firstname.lastname@example.org, 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 I guess the former page recipes do no not work because they are outdated.