I'd be interested to see the 'science' of this, in terms of which studies, by whom, and what they actually said rather than how you have chosen to extrapolate and synopsise. In any case, I think that to go from People with left leaning views more frequently come from broken homes, more frequently suffer from mental disorders and more often display narcissistic traits, to That data suggests, that their "activism" is performative is something of a stretch and possibly more your interpretation of the data.
Just as one EG: if deh leftists come from broken homes, that would generally tend to suggest they will come from lower rather than higher socioeconomic strata, simply because broken homes in general have poorer economic outcomes. Classical 'leftist' themes of 'fighting for the oppressed (I'm deliberately simplifying) are pretty easy positions to come around to if you have started from a non-privileged position yourself. Or, at least, they are if you have empathy, and herein lies the crux I suspect.
The dismissal of 'leftist activism' as 'performative' just strikes me as the typical reductive characterisation that 'Deh Right' does, seemingly unable or unwilling to believe that empathy is a quality that is available to their political opponents (i have no idea of your political stance, I'm just speaking in general terms). We condemn the other side as 'virtue-signalling' when they show passion for the problems of others, but when we do it, why, that is deeply-felt, and deeply sincere, and issues from a vast well of empathy deep in my soul.
Anyways, I don't think anything in what you said really points to the activism of deh left as performative. i mean, whatever report/s were or weren't behind the 'science' here, I'll wager the conclusion of them really wasn't 'so we can see here that Deh Left's attitude of empathy for others and the most oppressed is empty and performative'