I'm eternally turning over in my mind the world where fitz, and we the reader, meet the fool as a woman (calling her amber for shorthand's sake, though I think she would still be the Fool) before meeting the fool as a man. So many layers of it. To be clear, she is still the exact same gender, we have just met the other version first.
First of all, obviously, I do think we would have to contend with whether fitz would knowingly fall in love with amber in childhood, and have an earlier understanding of the incompatibility of this relationship with his one to molly. Or, whether the jester status and oddness still degenders a person enough that he doesn't place it until adolescent era fool in AQ. I think there's already edges in RA (in realisations like the 'bird boned' stuff) of the fool being looped in with Molly and Patience/Lacey (and Kettricken but she straddles the line in the same way as the Fool I feel) as the (female) loved ones in the palace whose safety he should worry about, but I wonder if that would be something fitz takes on earlier and more seriously.
But I do find myself thinking sometimes like, is Fitz isn't 'not in love' with Beloved because he isn't in love with them - or just because they're 'a man'. So if they aren't a man to Fitz then... Fitz is in love with them. (Perhaps part of why Amber is so discomforting...) Even though, the absolutely essential fact here, their gender would be absolutely no different in reality, one side would just be the more familiar one.
I also think that if the reader and Fitz met Beloved as a woman first, both would struggle perhaps even more to take seriously the possibility of their masculinity as a sincere part of their identity than they already do their femininity. It's much more unfamiliar both in the genre and in the world Fitz lives in, imo, for a man to pretend to be a woman, whereas a woman pretending to be a man is within this conception. I think both the reader and Fitz could see a logistical reason for the Fool to pretend to be a man, in a way that Fitz really struggles to see why the Fool would go for being Amber. And also, Amber is maybe taken as a more ready indication of queerness than if we had known the woman then the man. For example the average reader doesn't take Althea being Athel as a representation of her identity, but more people do take Amber as such - and obviously the narrative presents these two as different, but even so I think it's illustrative of the different tropes (and obviously the flavours of misogyny/queerphobia) at play.
I also think, obviously, because Fitz thinks of Beloved first and eternally at the end of the day as a 'he', this will always colour the reader's vision - I think this plus like, society, means that the average reader sometimes struggles to take what the Fool says about gender as more than a philosophical position.
And therefore Fitz (and perhaps the average reader) would be dismissive or not understanding of what Beloved is trying to communicate in a different way, I think. Fitz certainly would feel threatened by the implication on a quarrel scale level, because if they're a woman who Fitz loves in every way who could be a man - who he is perhaps more open to because of this impression - that may feel to him even worse of a deception, in an in-world and real homophobic/transphobic stereotype. Both perspectives are laced with misogyny and homophobia, obviously, but tinged from different angles.
Idk, in the immortal words of mercymorn the first. I often think about this.