Would you stick with a spouse who disrespects your parents/family?

It's really hard to tell, but definitely it should be a NO! Like what everyone else here has mentioned, you are all family now. If he isn't open to being civil at the very least, there's no chance for you to be together. It will keep coming back, trust me. Your family is still family no matter what, and you shouldn't allow anyone, not even your spouse to show any sign of rudeness.