not all intersex people are trans just by virtue of the fact that they're intersex.

I did not say that at all. You misread me. You claimed that "most intersex people have a binary, cisgender gender identity."

If you are cisgender (denoting or relating to a person whose sense of personal identity and gender corresponds with their birth sex) as an intersex person, you would be of non binary gender. I'm absolutely not saying all intersex people are trans. I'm saying they can't be all three of: binary, cisgender, and intersex. By definition. It is impossible.

Sex does not equal gender, and intersex does not automatically equal trans.

Nor did I claim this. You should read my other comments. I've never said any of these things. You are talking to a straw man.