What are the guidelines for showing proof of active duty status when asked by a senior enlisted member and both are wearing civilian attire?

When challenged by proper authority you are required to provide proof of status by showing your ID card. An NCO issuing an on-the-spot correction would, in my estimation, qualify as proper authority.
When the marine displayed an insubordinate and disrespectful attitude, and then compounded the matter by lying to an NCO (who I assume had properly identified him/herself), that young marine committed several offences under the UCMJ - two of which are fairly serious, court martial offences. If you can identify the marine in question, you ought to refer the matter to that marine's commanding officer by formal memorandum sent via your chain of command, up and over the top and back down so it will not be swept under the carpet.
Sounds to me like this marine doesn't want to be a marine. Perhaps the Corps should accommodate him, with a stop at the brig on the way out.

The SgtMaj always knows, and if not he knows where to find out. The BN Legal folks or Legal Services at CLG can answer by the book as well. The problem will be locating the offender. My guess would be that you are on duty 24/7, and when asked to show ID you should. Charging SNM will depend on how the SSgt presented himself, and locating SNM. The closest I got to this was in Greece. A Marine was trashed in broad daylight. Not a crime unless you're acting up, which he was. I showed him and his buddys my ID and gave them a lawful order to escort him back aboard ship, before he got himself in trouble. I'm not sure he even remembered it the next day, because at the time he was even belligerent to me. I discounted it to cheap beer and ouzo, but at least he didn't wake up in jail or not at all the next day. I checked the Liberty Log when I boarded later and verified that he was in fact aboard. Case closed.

You left out a lot of factors that would help us to provide insights. Bottom line is that you are a Marine 24/7. When asked for your ID you should identify yourself and show your ID. Again, too many parameters missing for a solid answer.