What Marine regulation or policy covers clothing on installation or in facilities?

Marine Corps Order (MCO) P1020.34G is the Marine Corps uniform regulations, which includes civilian attire. It covers revealing clothing (or lack thereof) under Para 1005.2, and also specifies clothing suitable for an occasion. This is normally regulations for Marines, but since you were entering a Marine Post... The MCO also charges local commanders with publishing local standards, so you may want to check on the Base Order if you are really curious. So, in answer to your question, yes, an actual order, and also a custom and tradition thing. If we didn't have stringent uniform regulations, our 1st Sergeants wouldn't have anything to do.

Usually the base civilian clothing policies are specific to the base written by the Base CO, or there is a region instruction with individual bases adding to that if they want. For example, Kaneohe Bay here on Oahu seems to have stricter requirements for civilian clothes wear that the other bases on the island.

I was in the Army, wish I had an answer for you. I can't see it being a policy but you never know.