Are you sure about the contempt and dislike? When I hear somebody say something stupid at work I won't necessarily say anything, or say what I think, but I will change my like/dislike of that person.
I think he's explicitly saying _expressed_ contempt and dislike: "Probably the fact that it is a workplace and we all want to keep our jobs serves to keep a lid on it."
If your only interaction with them is the disagreement, it's far easier to assume they "are stupid" rather than just "have a different opinion."