The problem is that "biological man/woman" is a nonsense pseudoscientific term. There's multiple forms of sex determination: chromosomal, hormonal, and phenotypical, for example. And none of them necessarily reflect gender, which is about how the brain develops.
Chromosomal sex is what most people think of when they use terms like "biological man/woman" but the chromosomes themselves aren't nearly as important as the SRY gene which, if present and active, triggers an embryo to develop hormonally and phenotypically male sex characters and male gender. But the SRY gene isn't always where it's supposed to be or working how it's supposed to work, which can cause mismatches between sexual development and gender.
And that's only one known potential cause due somebody to be transgender. There are more that we know of, and probably more that we don't know of.
So yeah, "biological male/female" is a gross oversimplification to the point of being straight up bullshit.
That's how it's going to be as long as we continue to use First Past the Post voting.
And since the only people who have the desire, and potentially the power, to change that are Progressives who caucus with the Democrats, vote Progressive in the primaries and Democrat in the general. If you're not willing to do that, then yeah you might as well get comfortable with the current system.