The guy's answer wasn't given or posted so we don't know how he explained his comment about "the right people". My guess is "right people" = legally registered voters.
Except for those in transition, the trans ID thing is confusing to me. If you're living full time in the gender opposite your birth, why would you be walking around with an ID that has your birth name or an old picture? Would a transwoman get all dolled up then go out and greet people sounding like Barry White? If she doesn't want to be outed, I would think, "NO!"
I understand the problem while you're in the process of changing everything but if you're going out to vote and your IDs don't match your presentation, revert to the old self, vote, then go home and change. I did just that until my IDs were corrected. And life went on.