You are understanding more than you let on, as i think your 'sauce for the goose' question is absolutely spot on!
Apologies for the legalese. In discrimination cases, when a state law is being challenged under the 14A equal protection clause because it treats groups of people differently, the court applies one of three standards of review (though the phrasing changes a bit over time): (i) for race distinctions, "strict scrutiny' which requires a compelling state interest and the law be narrowly tailored to address it; (ii) for sex distinctions, "intermediate" scrutiny, which means an important government interest and a law substantially tailored to it; and (iii) for everything else, 'rational basis' review, under which the law will be upheld unless the legislature acted irrationally (and by that, i mean, not even plausibly rationally) and within the scope of common law police powers. Here, the 6Cir and the state argue that the law doesn't even make sex-based classifications - it regulates puberty blockers and other transgender therapies regardless of the sex of the patient -- and thus 'rational basis' review applies. (IMO, this part is a little flimsy and a bit of linguistic sophistry and might well be struck down). My point earlier was to be careful about getting hung up on modern distinctions around transgender and sex -- because if the former isn't part of the latter, you're asking the Court - this court - to apply the 14A EP clause to a new type of protected class rather than just treating it as a form of "sex" discrimination (a bridge they've already crossed). And if they're not willing to do that and TG cases get addressed via rational basis review, it will be extraordinarily difficult for TG advocates - or per your hypothetical, either side really -- to challenge state laws in this area.
So, if this ends up as an intermediate scrutiny case (ie, the court rejects the state's rational basis argument adopted by the 6th circuit), it may still be the case that the state "wins" (I'd see ACB potentially "flipping back" to the conservatives more than NG), but more simply on the basis that states do have substantial police power interest with respect to medical care and minors (consistent with the way things sort of work out in a post Dobbs era).
