I'm not sure, but I don't think that the "you're not a real woman" asshole necessarily thinks the letter-writer is trans. The asshole is gender-policing (which is inherently transphobic, of course, as well as misogynistic, homophobic, and totally fucked-up). The letter-writer stood up for what she believed in, therefore she's not a "real woman" and deserves to be raped.

That kind of thing has been directed at me plenty, from people who know that I am a cisgendered heterosexual woman. A woman who doesn't roll over and play dead for the boys isn't a "real woman", according to the gender police. Therefore you can call her anything and do anything you want to her.

There may be some further story that I'm missing behind this -- maybe that vile commenter did get the impression that the letter-writer was transgendered, somehow. But people like that never base their insults on facts, only on their ideals of what men and women "really" are. Anyone who doesn't conform to those ideals in every respect challenges the gender cop's worldview and must be pounded into dust.