The argument against worries that men will claim to be trans to do weird shit has always been that no one would go through the process just for that, and that's true, but it stops being true if you remove all barriers for entry.
That's not my argument though. My argument is that if you want to stop people from transitioning to another gender just to gain access to privileges, the obvious solution is for everyone collectively to stop giving people privileges on the basis of gender, and as long as gendered privileges exist, it's FUCKING GREAT! for everyone to transition into whatever gender gives them the privileges they value the most in principle (besides the obvious downside that you'll probably give yourself gender dysphoria by physically transitioning if you're cis, which is awful).
At the same time, you have this political fight where conservative people think this entire thing is crazy, and supposedly the argument is that there is a really awful thing happening here with depression and suicide rates through the roof, and this intervention is one of the only things that has a proven track record of helping at least some. Do you not see how softening the trans label and removing all barriers of entry makes the entire thing that much less credible? I think I brought up this type of argument before and didn't get any daylight at least with faust, but I continue to think that fighting the political extremes on your side is one of the most important things to do to win elections, and conversely, making the extremes more extreme is one of the most damaging things.
I think this is multiple separate issues.
Firstly, although we might for pragmatic purposes want to use certain arguments to most effectively convince people or to advocate for certain configurations of society to most effectively push society in the direction we want it to go, we should not confuse those arguments for the most correct beliefs nor should we confuse those configurations for the ideal configurations. It might be the case that the best way to convince conservatives about trans rights is to tell them X, but it does not follow that X is something we should believe ourselves.
As long as we are talking about what should be argued and advocated for:
Most conservative people actually either don't think the entire thing is crazy or aren't particularly bothered by it being crazy even if they think that. They're worried about a few individual aspects of it if you bring it up, but they probably don't even spend a lot of time thinking about those worries otherwise. The depression and suicide rates are not where you want the conversation to go, because conservatives will obviously assume the causality is in the "transitioning causes the suicide rates" direction, so by taking the argument to that territory, you're already making it an uphill battle for yourself and might just end up making the conservatives more convinced than they previously were that this transgender stuff is dangerous and should be disapproved of.
If your goal is to get elected, especially to a low granularity position like the president, then being the most boring centrist possible is great. If your goal is to influence politics, being the most boring centrist possible is useless. To move the Overton window, you need the whole spectrum of views from slightly-to-your-side-from-center to crazy people who support a completely bonkers version of your side that isn't remotely socially acceptable, and various people on that spectrum will need to play their roles appropriately with respect to where on that spectrum they are. Blindly spending a lot of time criticizing the extreme people on your side moves the Overton window in the wrong direction, so you have to be careful about how you do it. For example, The Amazing Atheist now
thinks of it as a mistake of some sort that he, as a progressive, played such a major role in establishing the "anti-SJW reaction video" genre on YouTube which he did mostly because it was fun to criticize stupid stuff, and obviously the outcome of that didn't help progressives very much: instead of having conservatives discover these videos and develop more favorable views about progressives as a result, conservatives discovered them and most of those channels became radically more conservative to keep their now conservative viewers happy.
And it also just muddies the waters. You're lumping two completely different things under the same label; this is just bad instrumental rationality and bound to lead to problems like people following the wrong advice.
This we agree on (except I seem to think it is a lot less serious than you do).
And for what? That's the thing I come back to. If it was important to do this, then maybe. But faust literally likened it to someone getting a haircut. If the positive stakes are that low, then yeah, it seems to me that allowing everyone into the fold is a huge net negative. I feel each one of these three reasons ougweighs the upside by itself.
(When I say don't open the fold I obviously(?) don't mean misgender people; I'm going to use the pronouns anyone tells me to use every time without question. But I don't think / don't yet have been presented with the positive case for why it would be a good idea to encourage people to identify as trans.)
It's a little unclear what you actually mean by "allowing everyone into the fold". If your argument is literally that we shouldn't
encourage people to identify as trans, then I agree because I don't think we should be trying to influence people's gender identities in any direction, but it feels like I'm agreeing with a motte rather than your actual position.