It is not prejudice to consider a person who murdered 2 people to be dangerous. It is common sense.

Being schizophrenic doesn't make a person violent. Being mentally ill doesn't make a person violent. Some schizophrenics are violent, while some aren't. Some blondes are violent, while some aren't. Some people without psych diagnoses are violent, while some aren't. Some Republicans are violent, while some aren't. Some Greeks are violent, while some aren't. Some Norwegians are violent, while some aren't.

This guy has two problems. He's mentally ill and he has demonstrated a capacity for violence. I see them as two separate problems. Maybe he will not be violent again. But the O.P. is not in a position to evaluate that.

To get involved with this guy to see what he might be like now is not very considerate of him. Suppose the O.P. continued a relationship, got to know him better and decided he was not someone she wanted to continue dating. Deciding to withdraw from the relationship might be extremely stressful for this guy. He might be destabilized by someone holding out an offer of a relationship, only to withdraw that offer later. I would not want that responsibility.

Dating is a process of "trying someone out" to see whether or not they suit you. If they don't, you move on. I don't think you do this with someone who has a history of being severely unable to cope. I don't think that's being very responsible. And I think it's stupid.

BTW, I've worked in corrections with mentally ill inmates. I'm very much a proponent of people getting what they need, as human beings, regardless of their crimes. This young man has a right to a warm bed to sleep in. He has a right to nourishing food. He has a right to a support system of counselors, doctors, and peer groups to attend. He has a right to not be left isolated. He has a right, IMO, to know that responsible people are concerned for his welfare. But he has no automatic right to a "girlfriend."