You raised their trans status. What do even know of their medication?
Statistically the common thread for mass shooters is their love of guns. Deal with that and the number of shootings will fall.
Discussion
I take it you aren't aware of the link to psychoactive medications in mass shootings. And while we don't know those details yet, the vast majority of trans people are also on psychoactive medications.
It's a much stronger correlation than with gun lovers and mass shootings.
But depressed people, manic people, all sorts are on those meds.
If you want to argue that people on meds shouldn't have guns, we'd be in complete agreement.
But the reason most trans people are on meds like that is because society makes life pretty hard for them, not because of anything inherently trans. As can be seen where societies have a place for trans, or just don't make it an issue.
Also, corrolation cuts two ways. there is a 100% corrolation between people who commit mass shootings and who like guns. There is a much lower one if you run it the other way.
Lets agree that only healthy well balanced people should be able to have guns, and those who are on meds, for whatever reason, probably shouldn't. (This is pretty much the UK legal position. Need those meds, gun licence lost. And scandal when ill people keep it and shoot people, like in Plymouth a few years back)
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.