There was quite a lot wrong with this paper, and it wasn't about the "orthodoxy." The study makes claims about children, but the study was actually a survey of how parents felt about their children's transition. There was significant bias in how parents were selected to participate in this survey; it was predominantly advertised on anti-trans websites. The survey itself was biased. By all accounts, the statistical analysis of this data is not in dispute. The methodology, however, leaves much to be desired.
I read both the Federalist and the Huffington Post, because it's interesting to contrast how issues are being presented in mass media (and I get a certain pleasure in exercising my bullshit detector). But I certainly don't link to them in pursuit of a reasoned argument, because they're both quite biased.
https://www.marketwatch.com/story/how-biased-is-your-news-so...