I'm very biased because about 18 months ago I left my ex husband, who is an alcoholic and a diagnosed sociopath. I had to rebuild literally every component of my life with my own two hands and I'm grateful every day that I got my health back and that he has no children, while I have a real shot at starting over.

Some mental illnesses are destructive to everything and everyone around them. People with these illnesses should not be romantically involved with anyone and they should not raise children. I would argue they should have limited and supervised time with all children, period. Sorry, life isn't fair and no one deserves a partner. Not everyone is fit to have a partner. If you want to share your life with someone, you need to accept that it's a big responsibility for the other person and you should not hurt them. Some illnesses hurt others, that is the nature of the illness.

Also, if someone knows what they have and is lucky enough to have medication or other instructions to follow which keep that illness under control, they better same well be proactive and managing their illness, asking for help, etc. It's one thing to ask for help and show you're working on it, it's another thing to ask for help and use it as a crutch or not actively try.

People with physical illnesses learn how to manage themselves and take medicine, go to the doctor regularly, etc. Why should the responsibility be any different for those with mental illnesses?

This leaves out a third category, which is those who have illnesses that are largely unknown by them and/or the medical community, and people with illnesses that affect their conscious decision making skills. Those people are in a while other boat and I don't have an answer, but as long as they're not hurting others, I don't see an issue with it.

Tldr- handle yourself like an autonomous adult (even if you can't be, just trying goes a long way), ask for help, work on it and don't hurt other people and you're golden. That's all you can expect of any good person, really. Plenty of mentally ill people are genuinely good human beings. But if you can't do the above things, then no one deserves to suffer by being with you.