IMO (and IANAL especially not of constitutional law) the executive branch has to prove to the courts that it has a compelling interest to keep such registries and that its need is such that less invasive recordkeeping would not serve that justifiable purpose. E.G., it needs a registry of voters to determine if someone is eligible to vote and in which jurisdiction, because without it the pollworkers would have no way to tell.

Under Strict Scrutiny, laws enabling such registries must be “narrowly tailored” (E.G., voter registration doesn’t need to know how much taxes you pay and your tax record doesn’t need to know which party you’re registered to) and employs the “least restrictive means” necessary to satisfy its compelling interest (E.G., they can’t charge you a fee to update your voter registration and there will always be a free option for filing your tax paperwork).

Keeping lists of trans folks serves no compelling interest, is not narrowly tailored to the interests it supposedly serves, and there isn’t even a civil means of determining whether or not one is on the list (to say nothing of correcting it for the folks that have undoubtedly been added to it in error). As such, it is prima facie unconstitutional.

Even the lowest bar of constitutional scrutiny, “Rational Basis”, would require that the law allowing the list be “rationally related” to a “legitimate goverent interest”, and I can’t think of anything less legitimate or rational than a government’s claimed need to get into everyone’s pants.