"Anyone with a vagina" not too hard of an answer.
If you want to be a woman but we're born with a penis get safe and legal MtF transitive surgery.
Yeah does it exclude non-transitioned folks? Yeah but it's a clean and clear line to draw.
That is a compromise that will not satisfy most conservatives. It definitely doesn't address the "trans athletics panic" talking point (though it would be funny if they believed that the penis is what gives men a strength advantage), and I doubt that it would satisfy the "trans bathroom panic" talking point either, as they would likely strain to point out the lengths that sex offenders go to in the first place, inadvertently veering tantalisingly close to reality for a moment, only to conclude something like "their LGBTQ'ishness makes them do it".
To your average conservative, it wouldn't matter if a person had every medical treatment known to humanity to aid the transition and every scientific test devised determined them to be their target gender, because they believe as Fight Club puts it, "stuffing feathers up your butt does not make you a chicken".
The biggest issue with such a compromise (aside from the fact that it's not a solution with a scientific basis), is that conservatives need to believe in their inherently elevated status in the world. The existence of transpeople challenges yet another of such beliefs (this time being 'men are superior'), so transpeople have to suffer.