One of the problems with threads like this is that there are a lot of people talking *about* trans women, but very few people talking *to* trans women, let alone listening to them. And I'd guess there's no input to this thread *from* trans women. So far, at least.
First, to the main story: I don't know this person, I don't know their motivations, I don't know their story. I only know that this person was convicted of rape. Common sense is all that's needed here to tell you that there's no place for them in a women's prison if doing so means that the safety of the other prisoners cannot be guaranteed. That's all. It should be the same for any sex offender, or other high-risk prisoner. No self-ID laws, no Gender Recognition Certificate, can or should change that. I'd personally argue that it says more about the prison system, that the safety of prisoners can often not be guaranteed, be it from common or sexual assault, and that needs to be addressed -- but certainly, a person convicted of rape doesn't have any freedom to be in a position to rape again, or even have the opportunity to do so. It's a tragic case, but it's simply wrong to use this as a framing for discussing transgender people.
Secondly... yes. Trans people exist. A trans woman is a transgender person who identifies as a woman. A trans man is a transgender person who identifies as a man. It's not a question of surgery, or chromosomes, or anything else biological; of course, these things strongly correlate with how a person sees themselves and how they are seen by others, but they are not necessarily the same. Indeed, this insistence on interacting with people only on things you can't know, but only assume, seems so reductive. Why does it matter whether a person is XX, or XY, when you never tested this? Why does it matter what's inside a person's underwear when you'll never get to see it? This is what gender is about. It's your prerogative, I suppose, to care exclusively about a person's chromosomal make-up, but it's not an objective rule that must be obeyed.
As a matter of fact, too, I've spent a lot of time interacting with cis women, and I never encountered a problem yet. They've all seemed eager to welcome me to the sisterhood, be it as shop assistants eagerly helping me to pick out the best clothes and make-up, or all my women friends being instantly accepting, or welcoming me into women's spaces, etc etc.... I honestly find that it's the *men* in my life who have the biggest hang-ups. Well, that and people on this site. I can certainly see why if someone barged in to a women-only space, asserted that they were a woman, and brooked no dissent or discomfort at all from those around them, then there'd be an issue. But your problem there is because such a person is a disrespectful a-hole, not because of their gender identity per se. Women aren't under threat because sometimes they share spaces with trans women.
It's not an age thing either: I was at a concert recently, where apart from me I'd guess that the average age was in the mid- to high 60s. Either nobody knew I was trans, or more likely, nobody cared. Total strangers were friendly, we conversed about the concert, instruments we'd played as children, and one kind soul offered me and my friend a lift (it was very cold!). Mutual respect goes a long way.
I suspect part of this is because of the sad fact that, for most people, all they see when it comes to transgender people is stories like this one: someone convicted of rape, in all likelihood lying through their teeth in the (thankfully vain) hope of exploiting the system, making a mockery of trans people. But we just want to play an equal part in society, and be respected. That's all. It isn't too much to ask. Just be respectful.
Finally, on a minor point, I did glance at New Judge's explanation for parsecs -- maybe it's not perfect, but I honestly don't understand why ZebuSanctuary has been going on about it to such an extent.