For the vast, vast majority of people, it is. Which is what makes it a useful metric.
It is really not, though for most of human history a reasonably informed person could justifiably believe that; but even that hasn't been true for decades, at least.
I'm not against transgender, I'm just arguing on technical grounds. I don't see value in using gender-specific words if people can pick their gender, but I do see value in using them purely to distinguish between people by what is between their legs.
I don't think this really follows. There are still traditionally masculine and feminine traits, this is unchanged by people self-identifying as a gender other than the one they were born with.
If I am biologically male but identify as female, then guess what? I'm never going to become pregnant and give birth, no matter what mutilation of the English language I use to refer to myself.
It most certainly is. XY and XX are two things, therefore binary. Anything else is a defect in the individual's chromosomes.
So the fact that XX and XY configurations exist and other configurations are considered "defects" doesn't make biological sex a binary trait that correspondence to the manner in which gender is usually digitally ascribed and for which people are labeled "transgender" when their gender identity differs from that social judgement.