This is a really weird argument because it gets so many basic facts wrong. The most fundamental of which is the idea that taking finasteride means lower testosterone levels - it doesn't!
And I'm not even going into the issues with all the other confounding variables at play here, such as the motivations and dosing schedules for HRT being substantially different from other uses of finasteride.
I really don't know why you're bringing up data about HRT for transgender people that's nearly a century old in an article that's not about HRT, when we have plenty of data that's not only far more recent but far more germane to the topic at hand.
I'm bringing up trans HRT in the 1930s (got the decade wrong, sorry!) because the Nobel Prize for the synthesis of testosterone was awarded in 1939. That discovery was made at the start of our understanding of what happens when you muck around with sex steroids: "what effect does this have on mental health?" has always been a question that people have considered, and I was frankly shocked by the article's claim that it hadn't been properly considered in the US.
Of course, others have pointed out that this article is more of a hit piece than a scientific work, so it appears my surprise was justified.