I feel the Doctor shouldn't really be all that fussed about male vs. female anyway.
For sure, though I do remember the 11th doctor was scared for a second when he thought he had regenerated into a girl, so I think making a fuzz as a reaction was also possible.
But to clarify, I'm not saying the focus of the show should've derailed into the doctor being a woman. We're watching the show to watch him have space-tome adventures after all.
To be perfectly clear I didn't want the show to derail into a fetish show, but I guess I did expect they would seize the chance to do something with it, maybe a joke or two before moving on.
I agree it really shouldn't have mattered in the long run.
I get that you likely fear that the gender thing would derail the show as it does now, and yes it's likely that he wouldn't have cared at all, and I don't disagree, but my point is that if nothing would really change, then making him a woman is entirely pointless. Making him a woman needed some kind of story purpose besides "It's time for a woman to take the role!"
Him not caring at all is not mutually exclusive of it not mattering.
Honestly, even the doctor being indifferent to it would've been fun to explore. I could see one of is companions scolding him about him not caring about it all in embarrassing social situations everyone else takes for granted. Say, I could imagine a funny scene of him, now her, messing up her makeup like a clown, and not caring at all about it, only for a companion like Amy Pond forcing her to do it right.
Out of fear of repeating myself, I think the master's change to Missy did have a point. The master was actually a misogynist, so seeing him now being forced to be a woman was actually something that made sense to explore.
But with the 13th doctor? What was the point?
tl;dr instead of having fun with the idea they just wasted it to score woke points.