In other words, be disingenuous to the general public?

You know, the primary point of uniform messaging is propaganda--that is, to divorce people's acceptance of a claim from its truth value or the evidence for it.

When you have an adversary who uses propaganda tactics shamelessly, there are two reasonably straightforward paths to victory.

One: beat them at propaganda. Craft more believable lies, repeat them more fervently, play more strongly to deeply held emotions. Use truth only in proportion to the power truth has to sway people.

Two: expose their propaganda while remaining truthful. Rigorously adhere to what is true, carefully expose all flaws and exaggerations, paying special attention to exhibitions of bad faith (e.g. repeated presentation of factually wrong material after it was clearly shown to the presenter to be wrong), show how the adversaries punish their own side for going off-script in cases where they are either lying or not clearly correct (more evidence of propaganda rather than honest opinion). You don't play their game, you go meta and use that they are playing that game instead of seeking truth to defeat them.

The United States, and most of the world where trans rights are anywhere within reach, has government predicated on the idea that the latter is the better strategy. Democracies can't work if propaganda is generally the winning strategy.

In the face of anti-trans propaganda, I don't think a third path of presenting a public face consistent with delivering propaganda while nonetheless being fully backed by reason (save for suppression of public dissent) is a winning strategy. People willing to go farther along Path One will win, because propaganda works, and if you're not scrupulously clean, they'll effectively they-are-just-as-bad you (quantitative issues like degree of badness are just too hard to get across unless everyone is already calm and reasonable).

And you can see the internal dangers of Path One--any group that starts having strongly stated public answers seemingly ends up believing its own stories, getting caught by their own lies, and ending up divorced from reality.

And anyway, the right has been doing Path One for a long time; they're better, and they're on the anti-trans side, so that's a risky proposition that way too.

So overall--no, I don't think this is a great idea.

I think something very similar is a good idea--something like a Trans Bill of Rights, a solid well-considered set of positions that people can sign on to as a whole as being good without the requirement that they repeat the talking points whether they agree or not. Because the reasoning is in the Bill of Rights people don't have to compromise their own intellectual integrity to put on a public face that they don't fully agree with, or use arguments that don't resonate with them personally.

I'm overall very skeptical of the uniform stance idea. I think it both is bad strategy when faced with a propaganda-competent adversary, and bad for the community by encouraging members to divorce themselves from what they perceive reality to be (and/or fostering such incredible groupthink that everyone thinks the exact same thing within the group despite there being a wide diversity of opinion outside of it).