I've been thinking about this a lot when working on setting and world building for my own game. In a universe where anyone can change their body in nearly any way they want, any time they want, for any purpose they want, gender as we know it kinda doesn't matter. Or at least, gender and its connection to your body doesn't matter.
Hell, sexual identity, presentation, and everything kinda falls apart entirely at a certain point. Like, what good is the LGBT model when everyone can switch to whatever they want whenever they want. Trans individuals wouldn't exist at all, for example. Because they'd just switch their bodies to whatever gender they want to be, and that would be that. And it would be so normalized that no one would even give it a second though. And with everyone jumping between genders for fun, strict rules of gay/straight/bi stop being as important.
Identity politics, racism, matriarch vs patriarchy, and a ton of other concepts really do just kind of completely fall apart if everyone can simply be whatever they want to be. So you have to come up with new systems, which is fun.
It's really fun to write around if you really embrace these kind of universal attitude changes. It's an awesome bit of world building to explore, because its so completely alien to our world. LT doesn't really touch any of this, if anything it doubles down on gender norms even harder despite not really needing to.
While I get the sentiment of what your saying, in the spirit of philosophical conversation, I think your argument only works if your world is a Utopia. It falls apart completely once you realize that just because people
can change, doesn't mean they
want to change. Thus the only thing that really holds water is the fact that trans will no longer be a thing (assuming that changing one's gender is a cheap/easy/free process).
However sexual orientations will definitely still exist. I mean, think about it. Even if everyone could change whatever they want about their appearance/biology they may still be attracted to a specific type of biology. That person will basically just always seek out individuals who have that biology they are attracted to. And like I said before just because you can change to whatever you want doesn't mean you want to. For example, if someone in your world is attracted to the male sex, but the person they find attractive has female parts and prefers those parts, why would they want to change for that other person?
Racism will also still exist, because basically as long as something is different it can be demeaned. "Prey-only", "Blue Fur only", "Predators not allowed", etc. Sound familiar? Yes you can change to a prey animal type or transform your fur to blue, but do you want to? And even if we assume their are systems in place to prevent business/etc from doing that, you'll still have private entities and individual biases. "I don't like felines.", "If you enter my home you must be a flamingo." etc.
The thing is, even if we all looked the exact same, other things would change to discriminate. "Oh your from
that part of town."
Even identity politics would still be a thing. "I'm a feline so I do this...", "I'm a dragon so I act this way...". "I prefer being an eagle because it allows me to be myself..." etc. Unironically people may be even more likely to adhere to identity politics in your world in an effort to be unique, since the norm would be changing at a whim.
Again your situation will only work in a perfect world where everyone doesn't mind changing to be whatever they want.