The military is not monolithic.
The closer a military member is to dirt (or saltwater) and bullet-launchers of various calibers, the more likely they will be rather fundamentalist in their worldview. Especially if said military members are low in the hierarchy and LIKE being a basic rifleman or somesuch.
But the farther they get away from that, and the closer they get to high-tech jobs or things that require a large amount of 'G-2' (intelligence,) the more likely they are to being accepting - or, at least keeping their bigotry strictly to themselves.
Example:
I work on an Air Force base. People don't generally join the Air Force because they want to sleep in 'fart-sacks', in the dirt night after night, practicing bounding overwatch on the way to the two-way rifle range. The Air Force is pretty much a magnet for intelligent people who want to do something high tech.
There are the cops, though. The kids patrolling the base for the most part are freaked out by me. But those that have risen to positions of authority are, surprisingly, some of my staunchest allies.
Defense Language Institute by and large caters to the highly intelligent members of the military. I feel you are likely to have less trouble there than in a tract home somewhere in Generica.
And, I envy you living in a gated community in Monterey!

Karen