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I think you may be able to do some comparative analysis based on different rates of depression & suicidal ideation among homosexual youths both over time and across different states/local environments to get a sense of the magnitude of the social effect, but it’s basically impossible to fully disentangle social effects when evaluating the mental health of trans youth when you’ve got senators and governors proposing bills decrying them as ‘less-than’.
But, let’s try an experiment: let’s keep working on society until that’s _not_ the case, and if there’s still a substantially higher incidence of trans suicide in a world in which they’re supported and have care options available to them, I’ll owe you a coke.