This is not a great analogy, blue states do sometimes pass legislation that rhymes with these types of identity-based threats to gun rights. It is sometimes prohibitively difficult to get a CHL in certain states when your chosen name doesn't match your legal name. A few years ago Oregon almost passed an act by citizen referendum that would have had police precincts be responsible for verifying that identities matched licenses, with desk cops screening people's psych histories ("Uh, their license says Samuel, male but the document says Samantha, female? Oh and what's this, they're on several medications including a mood stabilizer? Denied.'). I'm glad that OP's poster isn't pitching their hypothetical analogy as a positive, but I want to be clear for the people playing team sports with their politics that identity-based rights abuses are all bad.

But yes, that Oregon referendum did get modified to remove the potentially abusive parts. And yes, it was because Republicans and libertarian types semi-successfully challenged it in court.