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But you're handwaving away the fact that conservative political parties are using trans existence as a wedge issue.
They can do this because, intuitively, many people think there's an advantage to be had. If there were such advantages, then we'd have to consider the thorny topic of what constitutes an "unfair" advantage, and whether the social implications of excluding a marginalised population outweigh the (perhaps disproportionate) impact of yada yada. But we don't have to consider any of this, because scientific research suggests trans women do not have such advantages over cis women: medical transition does not lead to a body configuration optimised for sports. Quoth, for instance, https://doi.org/10.1016/j.chest.2025.04.004:
> This study highlights substantial ventilatory inefficiencies in transgender women, likely associated with gender-affirming hormone therapy
This whole moral panic is an artificially-constructed wedge issue: they found something persuasive, and (by presenting trans people as something dangerous and new) side-stepped the need for evidence of harm, and positioned their reactionary bans as conservative. I think, when arguing about this topic, more attention needs to be paid to the fact that feminising hormone therapy (as a treatment for trans women) is older than insulin (as a treatment for diabetics). Any harmful consequences of trans existence (resp. participation in sports, etc) already happened, and nobody alive noticed.