LGBTQ+

Sure, but alpha is an arbitrary choice. An p-value of .051 isn't magically different than .049. They're essentially equally statistically significant. The reported p-value was 0.05. Smaller p-values are better, but its a continuum, not a series of buckets. Also, if you are testing if care is better than no-care, a 1-tailed test should be done, so the p-value would be 0.025.

But the bigger problem is they controlled indirectly for the outcome, so any difference is being minimized. And given they conveniently only leave out the valid model for specifically this section, it almost seems like the "mistake" was intentional. At least one author as a history of public transphobia and clearly had their conclusion before any analysis started. There's lies, damn lies, and then there's statistics. If you have enough data variables, you can find specific things where you simply do not have enough data to get your p-value small enough. Given all people in the study were at least referred to a gender clinic means they're in a good enough place where that's something they feel they can do any parents aren't able to interfere, its going to be a group with an already low suicide rate compared to the overall transgender population - they only have 7 data points divided between both GR groups. It would have to be a massive difference for any effect to be statistically significant and they still had to manipulate the data to bring the p-value up to 0.05.

Or I guess one could argue that death by suicide is caused by a high number of psychiatric treatment contacts, as the study's authors seem to be implying. Not saying you are arguing that. Just pointing out how ridiculous of a statement the study makes. Technically it just says correlation, but if you want to assume they're not just transphobic or totally incompetent, then that's the interpretation that would make most sense.