I would say it also depends on the bases. I have been on Camp Pendleton to apply for a job with a buddy of mine. We were both in suits and looking the part. Got to main gate. MPs never asked for ID or checked vehicle or papers. Just told them we were there to apply for Civy MP, and he (enlisted MP) looks at us like we were crazy, pretty much the look on his face was like shoot me now, I hate being and MP. He laughed and said you didnt hear me say anything, and let us on.
When we left, we went the back way out of Camp P, through the Fallbrook Naval Weapons Center, which we didnt know it was that road, but my GPS said it was the fastest route home. Hit the Navy cops Gate at the border line between the bases in an area where it military only anyway.
They pretty much said same thing, but told us if we wanted to pass, we needed to run 3 miles and do 50 push-ups. He then just said if we stay on the road we would be fine, get off and we would be lost.