There are two ways to argue against transgender accommodation policies: on the merits or procedural grounds. From what I've seen, conservatives routinely neglect the second approach and focus on the first.
I think that's because transgender apologists typically frame the issue in moral terms (as they see it), and conservative critics typically respond to them on their own terms. Up to a point, there's nothing wrong with that, but there's the danger of failing to challenge a false premise.
Secular progressives typically believe that if some group ought to be a protected class, if people ought to have a civil right, then the judiciary ought to discover that right in the Constitution, or the Executive branch ought to "interpret" preexisting law to extend legal protections to that new group. Secular progressives just assume that if something is a good idea (as they see it), then it's the duty of the courts or the Executive to make that a matter of public policy.
Problem is, that's diametrically opposed to our system of government. And it's not just a technicality. Empowering unelected bureaucrats with irrevocable job security to make social policy for the nation subverts popular sovereignty. That subverts the democratic process, according to which voters elect lawmakers to express the will of the electorate. And lawmakers are answerable to voters. Consent of the governed is predicated on rule by elected representatives who are ultimately accountable to the people who elected them.
Under our system of gov't, voters cede some power to the state, but it's a conditional grant of power. Voters can rescind it. Under our system of gov't, the Executive is not in the driver's seat, or the judiciary, or even the legislative branch, but the electorate.
The alternative is a dictatorship in which unelected judges with lifetime tenure and unelected bureaucrats with lifetime tenure impose their social vision on the masses.
Now, we should also challenge transgenderism on the merits, but my point is that, to some degree, that's a red herring. In principle, you could agree with the transgender claim on the merits, but still oppose bureaucrats in the Executive branch unilaterally rewriting statuary law through creative reinterpretations. If you think we need to create a new protected class, the proper procedure is to pass a new law.
It's important for conservatives to challenge the conditioned mindset that if something is (supposedly) a good idea, then it's a good idea to circumvent the legislative branch and impose that on the nation by judicial or Executive fiat.