I'm firmly atheist. I don't choose to participate in skepticism advocacy, but if I choose to, I might well prefer a pseudonym. (There are several fundamentalists in my management chain at work.)
I know of several people who are involved in the burner and pagan communities, who keep all of their non-mundane activities under pseudonyms. I don't currently know anyone involved in the SCA, but in the past I understood that many people didn't mix their role and real life.
I've been told that the BDSM community uses nicknames almost exclusively.
Many actors, musicians, authors, etc. work under pseudonyms, and would probably prefer not to mix their personal and public identities.
People being stalked (in real life or online) might have something to say, but not want to post under their real name.
Activists in the middle east and china certain prefer not to be forced to post under their real name.
Pretty much any individual or community that is subject to personal, social, legal, or political harassment may have motivation to operate in a public space, but use pseudonyms.
How about having a couple of flags, for "anonymous accounts" and "pseudonymous" accounts (the latter being "google knows my name and has verified it as much as anything else, but it isn't posted associated with this account). And indicate anony/psuedo accounts at the top of the profile screen. Add a security setting to block them entirely.