Absolutely yes, yes it does. You are very obviously treating gender rigidly, as you are treating it as a biological concept that can't be changed (at least not deliberately), so much so that you'd prefer medical treatments and all of society to treat gender as an anchored point that must be built around. It may not be a binary view, but it's rigid in the same way that racial essentialism is rigid.
That is not implied in what I said. Firstly, A characteristic does not necessarily have to be a "biological concept" to be either fully or mostly impervious to efforts to change it; Look at sexuality. Secondly, gender is tied up in identity and sense of self. We're talking about people who have no
wish to change their sense of self-identity, and such a thing cannot be forced from outside.
And then the very concept of transitioning adopts the rigid sex binary you think you're avoiding. The world has tall women and short men, hairy women and smooth men, low-pitched female voices and high pitched male voices, long haired men and short haired women, flat chested muscular women and flabby men... with the exception of genitals, the outside presentation of sex characteristics is tremendously varied and contains a huge amount of overlap, yet transitioning/presenting/passing all invariably involve pushing the individual toward rigid sexual stereotypes. A trans man goes with short hair and a deeper voice. A trans woman is more likely to shave legs and wear a bra. What are those things if not adherence to the strict sexual binaries you don't think you believe in?
This is just completely untrue. To equate hormonal/surgical transitions to "adopting sexual stereotypes" is to show a complete lack of understanding of both the process and the thoughts behind it.
Firstly, I don't know what you think is "rigid" about being able to change something of your own will. Most people would acknowledge that as the opposite of rigidity.
Secondly, a "deep voice" and shaved legs etc are what's called "presenting". A gender-nonconforming person may present a certain way by adopting characteristics associated with a certain gender, such as those. But those are not what we're talking about. We're talking about
physiological changes: hormonal, morphological (top surgery), sexual (bottom surgery). Those are not "stereotypes"; they're physical sexual characteristics.
People can change either: they can change how they "present", and/or they can change their physical sexual characteristics. The former are not innately connected to a biological sex, or even to a gender, they're just societally associated with a gender. The
latter are physically associated with sexual morphology. They can still be changed, with greater effort and some outside help.
I suppose you could say it's "binary" to say that breasts, estrogen, and a vagina are associated with the female sex, but that much is true. Those who oppose the "gender binary" argue that one doesn't need to have those to identify as a woman, and that people may change them if they wish. Both of which are also true, and are not mutually exclusive with the first statement.