You’re making a mountain out of a mole hill. I am sure ur prespective FIL didn’t mean it in that sense. I am sure he cross questioned your dad but not in the sense that he should mind. People tend to check each other’s families out since marrriage is a rishta between two families and not just two people. Your fiance is kinda wrong too in thinking that his parents are always right. Just talk to him nicely and tell him that you’re sure his parents meant the best but it might not have come out that way. Talk to your parents as well and make your fiance understand that too.
Secondly, grow up. Life and marriage is all about compromises and understanding each other and not make a big deal out of somethings. You and your fiance both should understand that and work to resolve the issues and not to create even more issues.