My girlfriend's parents don't approve of us being together. What does she mean by quitting? What should I do?

First of all, you have to find out why you don't agree to be together. What is the reason? You should "prescribe the right medicine" You can't just say that quitting your job will solve the problem. I don't know why, maybe not only her parents will have an opinion of you in the future, but also her girlfriend will have an opinion of you one day. Parents are kind to their children. As long as you show sincerity to her and her parents, I believe that one day they will see your kindness and accept you.