From the author:
"Descriptive studies aren't randomized controlled trials—you can't tell cause and effect, and you can't tell prevalence," she told Science Daily. "It's going to take more studies to bring in more information, but this is a start."
Clearly it wasn't meant to be based on any kind of scientifically repeatable methodology but simply to open lines of inquiry for further study, which likely won't happen now, given the backlash. Below you can see that the paper as written addressed those concerns you mentioned and more.
It didn't. She's handwaving problems away, not addressing them. You cannot get valid psychological data, even for a descriptive study, without at least interviewing some subjects directly. Likewise, if she knows that she's drawing from a biased pool of subjects then all percentages of population should either be removed or prefaced with a massive asterisk saying that it's only indicative of the population of three politically active websites.
It's not presented that way at all. It's presented as a preliminary study that is applicable to the general population, and it has some really, really big problems if it's going to be used like that.
If it's not supposed to be a scientifically repeatable methodology, then don't publish it as a scientific paper. Write an opinion piece. Write a case study. Write any of the number of other types of documents that don't imply that the information and data contained within has been subjected to rigorous selection and analysis. If it wasn't presented as a scientific paper, no one would care.
Don't get me wrong, I think it's an interesting enough topic and that someone definitely should do a proper study on it. But this one is bad. And I'm not talking about anything to do with the subject matter, I'm talking purely about how the science was done. It's bad science, and it's bad science that's attempting to pass itself off as something that it's not. It's entirely possible to do very niche studies and publish them with the appropriate provisos to limit their applicability, but that's not happening here. She over-reached on some pretty vague data from a poorly designed study, and now the scientific community is tearing her a new hole over it. That's peer review for you; occasionally it works as intended.
Psychology is a hard field in which to do good science. You're rarely going to get clear answers, it's always going to be hidden in statistics and as such requires very high levels of rigour. Historically that's been sort of ignored, and as a result all sorts of BS has gotten through. In the last five to ten years there's started to be a lot more push back against bad studies, particularly in psychology and other medical sciences. It can be frustrating, but it's ultimately for the betterment of the fields. Human psychology is already hard enough to understand without false information from bad studies muddying the water.
It's interesting the assumptions she throws out during that section you quoted though:
...this presentation of a socially mediated onset of gender dysphoria...
That's an assumption of cause and effect.
...the use of the drive to transition as a maladaptive coping mechanism...
That's an assumption that it's both a coping mechanism and that it's maladaptive.
She has her ideas of what's going on here, and she's looking for evidence of that. Which is fine, that's the standard scientific method; present hypothesis, look for evidence to prove it false. But that's not how the paper is written. She's gone broad, presumably because it's much easier to do a "soft" study like this where all you've done is send out some surveys than it is to do actual science to support or disprove a hypothesis.
. I suggest you post in the kids forum next time seems a perfect fit. I hear dumb dumb jokes there all the time.
