Out of interest, on proposition B why can we not claim that the presence of a Y chromosome in your DNA makes you a "biological male" and the absence makes you a "biological female". That should be a binary division. (Where these terms are only used in the contexts you describe as being useful; no disagreements there).
You absolutely can claim that, and it gives a nice clean division into two classes, that's sometimes useful and usually lines up with other assessments of sex and gender.
But it's not the only way to do it, and if you do that you won't necessarily agree with other people about a person's "biological sex".
For instance, there is a condition called "complete androgen insensitivity syndrome". A person with CAIS has one X and one Y chromosome, just like a typical man, and they produce male sex hormones much like a typical man does. (Maybe exactly the same? I'm not sure whether there are feedback loops that might go wrong.) But the cells in their body that are meant to respond to those hormones don't, and as a result a person with CAIS looks pretty much exactly like a typical woman does. Breasts, mostly-normal-female genitalia, not much body hair, higher-pitched voice, etc. But^2 they don't have a uterus, they aren't fertile (either "as" male or female), and there are internal genital differences that may have adverse consequences for their sex life if nothing is done about them.
If you just go by chromosomes, you will classify people with CAIS as male. But these people are all assigned female at birth, and they usually have no idea until puberty that there is anything at all unusual about their sex or gender. Their gender identity is almost always F rather than M, and they are generally heterosexual in the sense of being attracted to men.
So, what is the "biological sex" of someone with CAIS? I think several answers are defensible, but none is clearly correct or universally agreed. So "biological sex" is not a term with a clear-cut meaning in every case, contrary to "Proposition B".
