Like substance abuse issues, encouraging schizophrenics to fly is probably not the best way to collectively push for reduced medical certification oversight in GA.
Probably not, if that's the primary concern, but even there I don't think it will make much difference.
From a standpoint of risk to others, it's no greater than such a person driving a car. Probably less, due to LSA passenger limits and low vehicle weight. Remember, we're talking about someone flying as a Sport Pilot, not a person piloting an airliner with a hundred people in the back. The FAA has already mitigated the risk of operating a light sport without a medical by limiting MTOW, the number of passengers, the types of operations, and by requiring a DL and the FAA considers that sufficient.
Drivers operate cars while having virtually every medical condition in the book: sleep apnea, depression/anxiety, diabetes, heart conditions, etc., etc.. And while taking every med on the pharmacy shelf, too. And they're driving not just small cars but also trucks, vans, etc., and driving them in close proximity to other vehicles and pedestrians.
There's no reason to think the population of Sport Pilots, including those with higher tickets operating under Sport rules, is any different medically from the population of drivers. The FAA has decided that allowing that population to fly under Sport rules is an acceptable risk.
Furthermore, I don't think anyone is
encouraging a schizophrenic to fly. In fact, if I knew such a person I'd try to discourage them. But that's a far cry from seeking to notify authorities and asking them to take some sort of regulatory action against the pilot. Especially when the pilot has not (it seems) violated any regulation.
And on top of all that, what we have here, in this particular thread, is merely anonymous hearsay. That puts it pretty low on the credibility list.