The main reason all three superpowers don't want their citizens intermingling is that the war is a farce. The superpowers all use the war as an excuse to keep their citizens and countries under the proverbial thumb. It is also a reason to keep working so hard and producing the items they need to operate and survive...even if it produces a surplus that needs to be destroyed. Otherwise, the people of all three countries, if able to speak with one another, would realize that they don't need to work as hard as they are in order for everyone to have enough (food, supplies, clothing, etc.) to live. Part of the way the governments get what they do out of their people is by using propaganda and other brainwashing techniques to "hate" whatever country they're supposedly at war with at the time. If everyone made friends with everyone else, this "tool" of persuasion would be absent from their little box of tricks.