Playing nice with others

Fun fact: artificial intelligence wargaming is a thing, but military personnel are actively wargaming to prepare for see how AI will be used, and the best for how it can be used, in the future.  One interesting that has been discovered is that the use of AI sometimes has the effect of reverting a mind trained in analysis to its baser prejudices, a recent example being that an Air Force analyst will trust a program less if he or she learns it was prepared by a Navy programmer.

Why is it that our armed forces have such a challenge in respecting other branches? Is it as simple as football rivalries that extend into the professional sphere? Do organizations ingrain within their ranks their superiority so much that working across branches causes a sour taste in the mouths of all involved?  Even members of the intelligence community point out that former military officers now involved in covert action have run into bureaucratic roadblocks to missions being completed by members of the military who would not allow access to crucial resources, such as air support, for no reason other than an 'us vs them' mentality amongst allies.

How do we move to get away from this trap?  How can we move actual prejudice to truly professional rivalry?