I don't want to argue with Tequila as they are perfectly entitled to practice yoga any way they want. But I do want to comment on this thing they said:
...other than the chanting that the instructor does. He doesn't instruct on breathing, or linking mid and body with the breath, he simply calls out the next move so I'm not sure why it's so superior?
The mental aspect of yoga, and the breathing, are the invisible aspects that create all the difference. It's about learning how to focus and calm the mind, so as to listen to the body instead of our constant internal chatter. You can't see these things and that's why you (Tequila) say it's exactly the same, but it isn't. It makes all the difference, and it's what separates yoga from a normal exercise regime.
Further thoughts, relevant to the above but no longer replying to Tequila:
In yoga, the body is regarded as the physical manifestation of who we are. It's a given; we're landed with it. It might have a disability or a genetic illness or a sex we dislike , and that's what we have to work with. As someone said above: changing what we can, accepting what we can't change. Sex would fall in the latter category.
When it comes to gender identity, yoga teaching would regard this as not real. The mind is fluid, malleable, and in the realm of our control. Gender is just one of many attributes contained within the mind, and it's unhealthy to grasp any one single attribute and obsess about it. Basically yoga considers us all "gender neutral", non-binary. There's even a specific word used instead of non-binary: it is non-dual. A non-dual sense of self is the ultimate goal of yoga; that's what we strive for; so you could say it's an extremely gender-critical practice!
While at the same time respecting the body, understanding and optimising its functions, and being kind to it. Mutilating it would not be part of that.