Who gets to decide who's "healthy" or "well balanced"? I'll pass on that agreement.
You're making a statistical error in your causality statement, as well as the fact that mass shooters don't have to like guns. The share of gun owners who don't commit murder is higher than the share of psychoactively medicated people who don't commit murder.
I also don't think there's any credible evidence to support your claim that trans people are only on meds because society is so mean to them. If someone's trans in any major American city, the vast majority of people around them are falling all over themselves to virtue signal what an ally they are.