rjw4law says about some military bases: " ......... others couldn't care less " Well how much do you wanna make a bet, that if you asked (at those very bases) that you/he might not have gotten a "no"?
Here where I'm at, there are various military bases, both active and in-active (or I've hunted them before, during, and after). And yeah, sometimes you may get someone to "tell you otherwise". And other times you can go till you're blue in the face (as long as you're not some sort of nuisance - making messes etc....) and no one seems to care (assuming it's an "open base" to begin with).
They're probably like a lot of city parks, schools, etc...: Ie.: no one may care "until you ask". And it may also depend on if you're in a historically sensitive area, to begin with, and whether or not you're inside (verses outside) posted abandoned buildings, etc....