So, I think it's best we don't talk about "moral responsibility"...because truthfully, I would say that given Kashiwa's situation, and the expectations and obligations it involves, the "moral" thing to be doing is quite different from the direction of the resolution the story gave to us. That too is understandable, though. In both cases, the "moral" thing is not what's being looked toward to give them happiness as human beings. It very often isn't, I think.
Wait...so what should be the so-called "moral" thing for Kashiwa to do? You're not clear on this point at all.
The "moral" thing would be to not transition, to put the huge amounts of money and effort that endeavor would take into assuring her younger sisters' future.
Well, from a narrative point of view that's a horrible choice, since it's basically doing the same thing that drove Botan away, only several degrees worse. Not to mention, Kashiwa takes care of that to some degree by leaving college and finding employment instead.
From a moral point of view, I personally find that position abhorrent, since it places finances ahead of a vulnerable person's mental health, plus putting them under much greater strain likely to lead to depression and possibly suicide (both happen a lot in the real world). There's no way she could be an effective support for her sisters other than as a money-making machine under those circumstances, so there's no way I could support a morality like that.
It's been established in the story that Kashiwa's dysphoria is pretty strong, especially towards the end. And, I imagine, the consequences of the "moral" option you suggest would be equally strong.
If that's morality, I want no part of it and question whether it's actually moral at all.
So as I say, I think it's fine that Kashiwa is not pursuing the "moral" choice, but the one that may lead to happiness - for Kashiwa at least. One of the greatest truisms that struck me with this manga is when Kasumi said, in effect, "Nobody significant to your life is ever really going to be pleased by what you're choosing to do."
Indeed, that actually takes power away from the so-called "moral" choice since it doesn't really improve matters very much. And, as argued earlier, just the opposite for Kashiwa and those who care for her well-being.