This is flawed reasoning, principally because it rejects basic and fundamentally obvious truths, and accepts various leftist pro-trans ideological propaganda points instead.
First and foremost, 'peer reviewed' means nothing right now, not in and of itself. Before we even get into the reproducibility crisis, it has been proven for a good decade now that ideological fields of 'research' with their own journals publish and approve based primarily on ideological in-group, not actual science. A number of people, like James Lindsay, became mildly internet famous for demonstrating this by getting such 'scientific' journals to publish blatant nonsense.
If you want a scientific study that's actually reliable, you have to look into its methodology, the ideological bias of the people who conducted it, and who funded it. For example, one of the primary studies that pro-trans people liked to harp on about was funded by the company that produced puberty blockers, and was looking for a new market past just using it to sterilize convicted sex offenders.
Second off, gender dysphoria visibly and blatantly fails the sanity test far more profoundly than anorexia does. Anorexia is in significant part the result of over-glorification of slenderness for women, particularly given that genetics and build are a big part of what allows professional models and Hollywood starlets to be so slender. It's not hard to see why girls with builds that are healthy at heavier weights would compare themselves to that implausible ideal (impossible once digital editing gets involved) and feel like they are falling short. It's not healthy, but there's a clear logical chain.
Not so with sex/gender. Aside from the vanishingly rare actual case of intersex mutation (~1/60,000), there is no ambiguity about whether you are male or female. You may have more or less blatant characteristics typical for your half of the gender dymorphism split, but there's no ambiguity over whether you have testicles or ovaries.
In order to think that you actually are the other gender, you have to enter into an explicit and outright delusion. This means that it by far exceeds other disorders like anorexia.
Further, permanent harm from anorexia is fairly limited to the more extreme cases. With gender dysphoria, as soon as a child or adolescent is put on puberty blockers, serious chances of permanent harm starts to accrue. From weakened bones, to stunted growth, to sterility, to drastically increased risks of cancer. Once HRT begins, reduced fertility becomes functionally certain, outright sterility is highly probable, and flooding your body with hormones it shouldn't have can cause all kinds of issues, again, including higher cancer risk.
Once surgery comes in, the body is permanently mutilated. The stories of people who've broken free of the trans propaganda are absolutely horrifying. Permanent physical debilitation, ugly scars that are either impossible to remove, or impossible to remove without very expensive cosmetic surgery, permanent dependence on drug regimens to make up for what's lost, their genitals rendered incapable of feeling any form of sexual pleasure whatsover.
And that's before you get into the fact that their odds of finding a romantic partner who isn't into seriously warped fetishes (which would almost certainly involve pushing them back into trans ideology) have been almost completely destroyed. They're certainly never going to be able to have children naturally.
On top of all of this, you have the fact that thinking becoming the other gender is possible means you either failed high school biology, or your school never taught the subject properly. It certainly means that you've been lied to extensively by a significant number of people, at a minimum including medical professionals, probably including educators, possibly your parents, etc. That kind of betrayal will do enormous damage.
Adolescents who've been subjected to these horrors will carry massive physical, emotional, and mental trauma for the rest of their lives. Even worse, the further they've gone down the puberty blockers->HRT->surgery pipeline, the more perverse incentive they have to never admit that they let themselves believe a set of lies, and their self-destructive behavior is all the more likely to continue.
Anybody who has a basic working understanding of human physiology would have known the idea that you could be 'born in the wrong body' or 'have a woman's brain in a man's body' is utter nonsense from the start. Again, there is an extremely small percentage of the population who have strange development abnormalities, but they're rarely involved with 'trans' issues. Almost all the people who are have, or had, healthy functional bodies of their correct sex.
Gender dysphoria, like other drastic forms of dysphoria, is a tragic thing to suffer from. I hope that everyone who does suffer from it receives support and help in overcoming the mental affliction.
Pretending it is a physical, not mental affliction, and 'treating' it by supporting the disorder rather than trying to get them therapy to defeat it, is the exact opposite of help. It is turning an already harsh-suffering into a permanent crippling and mutilation.
And again, I cannot emphasize this enough, basic high school biology and human physiology are all that is needed to know it's all bogus. The pituitary gland is nestled in the brain, and is key to controlling hormones. This is covered in any high school that teaches human physiology properly.
A more detailed study of current medical technology would reveal that the ability to 'change' a person's sex isn't even remotely close to possible. Trying to force the change through brute drug/hormone therapy is incredibly foolhardy, especially because the only 'gain' from it is supporting a delusion.
If one starts looking into all of the technologies that would need to be invented in order to make such a thing actually possible, you go firmly into the realm of 'technology so advanced it's magic,' especially with how crude and full of side-effects attempts at genetic modification are, especially when it's not done at the 'just-fertilized egg' kind of level. So many people watch or read science-fiction that depicts incredibly advanced technology as routine and casual, that they lose any comprehension of how difficult a thing is, not to mention the many possible failure states.
Inventing transporters from Star Trek is about as likely as being able to actually properly change someone's sex. Maybe somewhat harder, but it's in the same general ballpark, because you need to rebuild someone's entire body, cell-by-cell. You're better off just saying you want a magic spell; it's more honest.
Then there's your assertion that deliberate suicide is not only a sign of greater mental stability than accidental suicide on the part of anorexic people (which again, was vanishingly rare to actually happen), but further that this is the fault of people rejecting and isolating 'trans' people.
This is also not only not true, but easily proven not to be true.
How do you think that suicide rates, both attempted and succeeded, compare between 'trans' people, and slaves, both historically and the less-well known people trapped in it currently? Or perhaps Jews in Germany/German controlled territory during the Holocaust? Or shall we say people trapped in extreme long-term imprisonment, even outright solitary confinement, by various tyrannical regimes, current and in recent history?
I've heard people quote suicide attempt rates as high as 40% amongst trans-identifying people. From what I've found, there is not a single other group in recorded history that had rates that high, no matter what kind of social oppression, denigration, outright imprisonment, or torture they suffered under. And, of course, such actually oppressed groups rarely had enormous wings of the culture they lived in, including government officials, most of the educational system, major corporations, etc, actively speaking out in their support and affirmation.
No, the suicide rate among 'trans' people is not a result of harsh treatment by others. It's the result of a horrific internal conflict of identity, and over something so fundamental to human nature as sexuality. It is far more compassionate and caring to encourage people to overcome that conflict and accept the body they were born into, maybe work on some self-improvement if that helps, than to sell them a lie that permanently mutilating and debilitating their body will help them.
....So no. 'Trans' people are not more sane and stable than those who've been anorexic, or had similar conditions. I could go on, but I have work to do, and I think I've made the key points well enough for now.