HI Cedar,
If your girlfriend were to develop schizophrenia, the earlier she got treatment, the better her outcome would be. If you have read my SharePosts, and Robin Cunningham's, you know that people with schizophrenia can be successful in life.
If you love your girlfriend and are prepared to stick with her through thick and thin, "in sickness and in health," as the saying goes, that's what matters.
I am sorry your parents have a stigmatizing reaction to your girlfriend's family. I really don't know what I can say about this except to say that in the end it's your decision. Marriage is a big step after six months yet if you feel you've found the one, you're a lucky man.
Best regards,
Chri