It is true that nothing is "beyond the realms of possibility" if you apply only handwave sci-fi magic to all situations. It is "within the realm of possibility" that the whole game is the MC being put in a holographic realm and none of it is real, but that would be highly unsatisfying.
Raene's whole story line might disagree with this. Her story would be solved the moment she escaped her father's reach. Yet we clearly see Raene taking some kind of hormone replacement therapy and not gene, let alone whole chromosome, alteration therapy. Modifying existing genes within existing chromosomes is not the same as transforming a chromosome entirely. It's like equating changing a tire on a FORD SUV to even another brand of tire to replacing the whole engine with an engine from a Chevy Impala. Theoretically it is possible, but it would be exponentially more difficult and cause too many issues to be worth the effort. Chaning an X into a Y or a Y into an X isn't just like shifting a little DNA priority about.
The barbarian women are largely handwave sci-fi magic anyway, but they are still fundamentally women and nothing about them is beyond the realm of even natural possibility other than only having daughters (since genetically it is the sperm that carries the determining X or Y needed to set the sex of the offspring). But even that is possible if a bit of genetic virus was given to them, for example, that kills any Y sperm or even fertilized XY eggs, or something like that. In fact, such a virus could naturally happen as well. A Virus that only attacks the Y chromosome has been used in other fiction before.
Changing X to Y after it is set is more akin to changing an apple into a mouse than just altering the existing genetics of a group of women and the eggs they produce in utero. While it is possible that Perv could handwave genetics like handwaving FTL, that is what would be happening, it would be sci-fi magic. Which is fine by me, I honestly don't care about hard science that much in my sci-fi as long as it is consistent within the setting from scene to scene. But that is the issue with this theory as I see it. It doesn't seem to fit the narrative being built, the existing technology of the setting, the internal logic of the setting, the real world applications and realities, or established actions of the characters involved (if you are using this to promote a justification for some theory that Agust is not the MC and girl's dad).