What a difficult, difficult situation. I understand that your parents believe they are acting out of love for you. They don’t want to see you getting more deeply involved in a romance that could lead to heartbreak. What they don’t understand is that a mental health diagnosis, especially when well-treated, doesn’t have to lead to all the dire things they think it will. Sadly, their fears have led them to say some very hurtful things to you. Do see it as their fear talking. What they are saying is not necessarily what they really believe.
At 20, you are no longer a kid who only has two choices: Go along with your folks or be defiant. You have a third choice: You can do your best to keep your head and to respond more maturely than your parents are able to. Explain to them, gently, that they did not raise someone who can’t be rational. Let them know that you understand their fears for you and appreciate the loving intentions. Let them know what you told me: That your boyfriend is taking charge of his illness, that he is on medication and that his prognosis is good. Ask them for their respect and support as you explore for yourself whether this is the relationship for you.
Do not get angry. Anger will only prove to them that you are an immature child who needs their protection. Stay calm and loving and give them some time. If that doesn’t prove effective, you have some hard choices to make. You are an adult and are entitled to make your own decisions. However, I suspect that your parents are helping you fund your education. That complicates things for you. Only you can decide what sacrifices you are willing to make to keep this man in your life. I hope it doesn’t come to that. I hope you can appeal to your folks to trust that they raised you well and that you can make healthy decisions.
I wish you well