The argument appears to be "wanting to change your gender posits that gender is part of objective reality and not a social construct, which is sexist", which is analogous to "trying to create racial equality implies the races are unequal now which is racist".
If you ignore realities of present society and pretend that things like gender roles and racial discrimination don't exist today, you can make it look like people are fighting to create those things instead of to reduce them.
The analogy is deeply flawed since nobody is changing their race to fight racist social roles. Just imagine going to a classroom and telling the audience that some children are born in the wrong body that does not align to their real, deep race.
Rather, we fight racism by rejecting racialized social roles. There is nothing racist in acknowledging current racial inequality, but it's deeply racist to suggest there exist a "real", inner race that influences our behaviors, and if society pushes us into racialized roles, it's because they don't afirm our "true race".
Similarly, we fight sexism by rejecting gendered social roles, biological sex is a minor anatomical detail that - aside from well specified domains, such as reproduction and raw physical strength - should have no bearing on someone's ability and right to perform any social role they desire.
To do anything else for pragmatic reasons is as if the suffragettes would have dressed up as men on election day and attempt to vote that way; ie, recognize and reafirm the restriction instead of attacking the fundamental inequity of the male-only vote.
Your first sentence suggests you're trying to argue, but I don't see where the contradiction is. Even the transmeds would agree with what you've written.¹
Trans people don't be trans in order to fight sexist gender roles. They're trans, and (often) fight sexist gender roles.
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Some pedantic notes that may or may not be relevant:
• The two different domains you list are influenced by different dimensions of biological sex, which can vary independently.
• A social gender, while culturally-influenced, seems to represent something fundamental about human experience.² Many societies' social gender categories do not align 1-to-1 with biological sex classifications, but 'most all of them have them. Meanwhile, race isn't seen outside racists and those influenced by racism: it is a recent³ invention.
• Some people's brains, for whatever reason, do care about the sexual characteristics of the rest of the body. This isn't much of a problem if that "preference" matches what the body is, but it can cause people significant distress when they don't.⁴ ⁵
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¹: Though transmeds would dispute the (perfectly valid) implication in your second sentence. "Born in the wrong body" isn't an entirely accurate explanation: it's more of a lie-to-adults, only required if you've got a stodgy old binarist model in your head that can just about conceptualise the existence of gay people. It's up there with "lesbian relationships are butch/femme": not something we need to be teaching children, though probably better than acting like LGBT people don't exist.
²: Disclaimer: I'm not speaking from experience. My intuition is that gendering is bad. From observing other people actually liking, and gaining value from, gendering themselves, I suspect there might be value in keeping gender around, for their sakes; however I have not really taken the time to square this with the clear and obvious harm caused by our society's obsessive gender-all-the-things-and-people tendencies.
³: Dating back at most 1400 years, with its European-coloniser incarnation probably not much more than 400 years old, and the modern eugenicist version less than 200 years old.
⁴: This doesn't necessarily even line up with gender! I know a cis guy who went on feminising HRT, and he says it made him a lot happier. (I don't have access to the inside of his head, but I'd be inclined to believe him.)
⁵: Personally, I don't see why someone should need to have a medical condition to get to choose what their body is like. I get the rationale, seeing as these are semi-permanent choices that one's future self might disagree with – but we could apply the same logic to tattoos, nose rings, or earlobe stretching. (Perhaps we should!)
Regardless, the fact remains that many people do have such a medical condition.
If you ignore realities of present society and pretend that things like gender roles and racial discrimination don't exist today, you can make it look like people are fighting to create those things instead of to reduce them.