In my experience, the majority in the military is right-leaning and religious. I am agnostic and tend to be pretty liberal myself (big Bill Maher fan). That said, some of my greatest friendships in the military have been with actively religous people and conservatives. Often, we have much more in common than we do differences. I think politicians intentionally try to create a spuriously contentious and antagonistic culture in order to rally their base. Some people really feed off that and can become insufferably obnoxious about politics. But most people in the military are good about being discrete with their religious and political views. I have to say that though it's uncommon, when I do hear politically touchy statements, it usually comes from conservatives. But I think the reason is that they are consciously or subconsciously aware that many people around them in the military think like they do, and so they feel more free to be outspoken. On the other hand, I think the liberal minded people can be equally annoying, but they don't tend to be as outspoken in the military since they're in the minority. However, it would probably be the reverse scenario if you were a conservative at Berkeley. In general though, I don't see it as a major issue.
I once had a patient who was a self-described "Wiccan-Buddhist." He also had a major personality disorder and had an addiction to S&M, and ended up getting Ad Sep'd out of the Navy, but the point is that you might be surprised at the amount of diversity in the military. I'm sure you'll find plenty of great people to associate with, on both sides of the aisle. There many other more profound reasons that should weigh in on your decision to do HPSP, but I know you don't want to rehash those.
Good luck with whatever you chose.
