You might have a good argument if you had a link to the research.

The most recent study I know has rates of 1:10k and 1:25k respectively (https://pubmed.ncbi.nlm.nih.gov/24982651/), with rates rising rapidly, and very low reports of regret for intervention (very low rates of regret would be unexpected if you're badly overdiagnosing people).

If you are getting better at diagnosing things that are pretty stable in the population, and people are losing the fear of even mentioning that they have a certain condition, you expect flat rates when you've caught up and diagnosed about half the missing part of the population; then the rates go down until you hit the steady-state levels needed to come up with the rate of new onsets of gender dysphoria (related to the birth rate, but delayed by varying amounts).

So--I'm not sure that your tenfold fudge factor is enough. The arguments about homosexuality don't really carry much weight, because homosexuality doesn't require modern medical technology to express itself, whereas without medical intervention, what are you going to do with gender dysphoria but survive with it (or commit suicide, I guess). There have also been plenty of accounts of transgender behavior (e.g. crossdressing) throughout history. That could be associated with expression of homosexuality, or with normal gender identity, but it could also not.

Anyway, as far as I know, there are a grand total of zero careful studies where they do unbiased sampling to estimate the rates; everything I've seen involves self-reporting followed, perhaps, by clinical diagnosis, which provides two places where cultural norms could have extremely stringent selection effects.

I agree that the fadishness is a concern. But you seem to believe that it's more likely that a fad can push up rates of something by a factor of a hundred (?!) than that cultural stigma and reporting bias can push something down by a factor of more than ten. That's not impossible, but it sure would be odd, given that both factors manifest the same way (i.e. via social norms), and the gender-affirming norms have been really strong.

So, anyway, don't just say there's a study. Link it!