the philosophy behind it reinforces gender stereotypes it seeks to combat.
I think it's worth saying that this is only true if we assume it to be true. Someone can feel gender fluid without changing their presentation much, if at all. Add to that, those who do have a presentation change are largely doing it because our species is highly visual, and I think you have your answer.
Remember that people fundamentally do judge people based on looks. We just do. I don't think anyone can honestly, sincerely tell me that they wouldn't assume a person was female if they were presenting in a manner that was clearly classically feminine. People are very visual and highly pattern-oriented, so we recognise that "long hair, shorter, in a dress = female". So... if you are fluid, then what can you change? Well, probably the clothing and any makeup you are or aren't wearing, right? You likely aren't going to be changing hair regularly, since that's not practical, and you can't change things like height.
So, if you feel comfortable being referred to as male today, then you have to use the visual storytelling language that our culture has provided you. If you want people to "see you as male", you need to use that language. They aren't going to see you as male if you wear a dress, even if you personally don't care. You're bound by the lowest common denominator.
So, saying it "reinforces gender stereotypes" is, I feel, placing the "blame" on the wrong person. Genderqueer people aren't intentionally "reinforcing" anything, but minority groups of ALL kinds are always beholden to the tyranny of the majority. They have to be "good minorities" to be given any kind of respect and recognition, and that's going to include trans people (both binary and nonbinary) being forced to adhere to gender roles whether they want to or not, just for a chance at recognition.
For example, until shockingly recently, if a binary transgender person wanted to get their gender legally changed, they were required to:
So... no kidding they followed gender roles! They had to!
This applies to nonbinary people too, but less formally and more socially. If a person wants to be seen as nonbinary, they "Aren't Allowed" to be "too" female or "too" male. There is a very specific dress code that society seems to have selected as "the androgynous one", and well... that's just not what most nonbinary people want. But, if you want people to accept you... you have to follow THEIR rules, not the ones you want to follow.
And then they blame you for "reinforcing gender stereotypes", and it comes full circle huh?
Simply put?
They aren't following gender stereotypes out of choice. The majority, who are unwilling to even begin to accept anything outside their immediate comfort zone, are forcing them into doing so. If they want even a CHANCE of being treated correctly, they have no choice but to follow the rules to the letter.
And then they're being blamed for it.
I'm not nonbinary, but I'm queer and I have pushed for a lot of queer rights movements etc. This is a common thing people ask, and it usually comes down to "do you think they WANT to do this?! Hell no!"