I am a retired reservist (6 years Air National Guard). Come to think of it, I believe we called them APs back then.
I have always been impressed with their politeness and professionalism. I know, however, not to speed at all on base nor violate any rules. IMHO, law enforcement on base is much stricter than off base.
I can remember during the Vietnam era, security at an unnamed base was extremely lax. Today, fortunately, that is not the case.
Back in the old days we were snowed in on base and built a big snowman on one of the side roads. The MP's came by in their jeep and rolled it over. We rebuilt but put in this large ship anchor that was on the lawn. We hid low as they had to go get the wrecker to pull them off it.