When an E-4 calls me "hey" or "hey man" knowing that I am an officer, should I bother to correct him?

Correct him/her on the spot, you will be doing them and yourself a favor by preserving the integrity of the rank! And call them to attention when you do it!

This should never happen. I always said to treat everyone with the respect due. I was assigned to an outside duty with a SSGT that I didn't know or normally work with. He used to whistle to get myself and two fellow CPLS and a SGT to come when he needed something. I respectfully asked him to consider the fact that we are all NCO's in the Marine Corps and deserved some respect for that, even if we were not Staff NCO's. I respectfully asked to be referred to as Cpl Howard or even Howard, as I am not a dog. I also pointed out that respect goes both ways and a good leader needs to deserve the respect, and not due to rank only. I think my talk made it to the Captain and I also believe that I was backed up on what I said. The whistling stopped.

Military courtesy extends to civilian attire as well, at least it did in the 80s. Sounds like this SPC is stretching the regs and needs some education.

You failed to do it at the moment so it’s too late. With that being said, “lighting someone up” should ALWAYS be a last resort. TALK to the troop and explain the importance of remaining professional at all times.

If you hold any type of rank of any military, you should always set the example. Correct any misbehavior no matter if they are under your direct supervision, you are a leader.

You really hunting for salutes out of uniform in Walmart?

You're worried about someone talking to you as a fellow human being outside of work and out of uniform? Seriously? Go ahead and "correct" the soldier then. Show him that you identify as your rank, even out of uniform.

No, you’re just an officer. You’re essentially civilians in uniform.

Why are you an officer to begin with? The Army and other branches demand good order and discipline to be successful. Not correcting a soldier who has no respect for authority and rank will call to question your future decisions and orders which could become fatal. Teach the soldier respect!

Apologies, did not mean to send too early.
Especially as a lieutenant if you feel that the issue is something that needs to be addressed, allow the soldiers NCOs to take care of it. If you choose to address the issue yourself don’t light him up over it. As other people have commented there’s a lot of details that people trying to address your question are not aware of. Off post in civilian clothes, he may recognize you but not know where he’s recognizing you from. Most importantly, as a fairly new Lieutenant, stepping too hard on him for something that seems fairly innocent as described is likely to be viewed as an overzealous Lieutenant who is insecure with his authority. That’s not meant to be a personal evaluation of you, just a normal enlisted response before getting their butt chewed by an LT. The SFC Who advised you to approach it with a I’m glad you feel comfortable talking to me but don’t forget to say “sir” response was spot on if you intend to handle it yourself. Just keep in mind that issues of discipline, in general, are best handled by the soldiers NCOs. Let them be the jerks, it’s their job. If the issue is severe enough and the NCOs are not handling it then you can step in. Officers trying to handle enlisted discipline issues without first involving the NCOs usually end up doing more damage not just their own reputation but the reputation of the officer core in the eyes of enlisted personnel. The other thing that occurred to me reading this and the responses after is I am concerned that you felt the need to ask this question on rally point. I’m assuming there are more senior and seasoned NCOs that you work with who would be better mentors and advisers then us random strangers here on the Internet.