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.
The correct pronoun is whatever people deem the correct pronoun is. Personally, I don't see a lot of value in referring to people as their preferred gender. I see more value in referring to them based on their biological sex.