An “intersex” person (now usually described by doctors or biologists as a person with a disorder of sexual development, or DSD for short) is either male or female, just like any other human being. So to use the rather silly terminology under dispute, “binary”. The “disorder” is a non-typical development of sexual characteristics of the person’s sex: a disorder of male development in a male, or of female development in a female. We can’t even mention the disorder without implicitly affirming the sex categorization that it affects. The “binary” is part of the definition of homo sapiens.
Every “intersex” person is either male or female. Many in that community object to others describing them as some kind of other sex and, especially, using their medical condition as an ignorant cudgel to advance the “trans” rights agenda.
This sounds like you're conflating biological sex (i.e., having both breasts and a penis) with gender (i.e., person IDs as female). I understand why; they use almost the same terms. However, it is important to note that, if you are describing a person who was assigned female at birth, and continues to identify as female, that's entirely describing their gender, not the state of their biological sex characteristics.
In other words, if a person experiences DSD, but self-identifies as male or female, what you are describing is not proof that sex is a binary, but rather proof that a person with DSD can experience gender dysphoria.
I don’t see where I’ve conflated anything, nor do I understand your attempt to show where I have. “Biological sex” is redundant; sex is a biological classification. There isn’t any other kind.
You argue that people who are intersex regularly identify as male or female, and do not like being pointed to as trans representation...but that's not describing their biological sex characteristics, that's describing their gender identity. You're describing someone who identifies as cis-male or cis-female, despite their biological sex characteristics.
Every “intersex” person is either male or female. Many in that community object to others describing them as some kind of other sex and, especially, using their medical condition as an ignorant cudgel to advance the “trans” rights agenda.