This advice is golden for other situations, but I was thinking though of how I could phrase the OP argument specifically. I'm targeting liberal progressives, like I was and mostly am. They'd see "women's sports" as a dogwhistle. I want to stay friends with them, HOWEVER I do not want to ally with the "hahaha equal lefts, libtards" guys among them. Conservative men are still traditionalists who believe in sex but then go on to believe in gender roles. Their issue with trans people is that they act in a way unfitting to their sex, not that they reinforce the association between sex (or, "sex") and character. I've never liked the radfem/conservative alliance, it brings radfems closer to a side that uses them as a prop while fighting against their rights.
Using sex-based oppression as a terf
argument isn't always that effective, since even TRAs like I used to be actually agree with it. Honestly I think even TIMs do also, (yet only when terfs bring it up first, funnily enough). They admit it but they still emphasize gender as what determines a man's sex. To them, gender is a social construct but that doesn't mean it shouldn't exist. Have you seen Contrapoints' video on gc? He makes the dumbest fucking comparison to gender abolition ever, to denying people political asylum to abolish borders. He says that abolishing gender would take away trans people's ability to be their preffered gender. Oh no, uwu! That's what you're dealing with.