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

USMC. I was an E-4, I had friend, a Full-Bird Col. We were on a first-name basis. Only, Only, Only- because he said we could When We Were Alone, on maneuvers, Out In The Middle Of The Mojave Desert. And Only after the day's activities were done and ONLY when we talked about religion and life. We both knew that using his first name Without his Express Permission was the epitome of disrespect on my part. Never Ever allow a subordinate to re-name you.

Irregardless of where you see him, its a sign of respect not only for the person himself or herself, but of the rank you HAVE EARNED just like anyone else has. I would quietly take the individual to the side and correct the situation immediately. If you let it go you have failed that individual as a person, subordinate and yourself as a leader.

If both on active duty, you're both active duty whether wearing uniform or not. Protocol should be consistent at all times in the strictest sense. Having said that, there are other inter-personal relationships/friendships that could happen when 'off duty' that might change things.

If you don't care why should he/she.

Might depend on how progressive the CRT Commandment is!

Is this ego driven or service driven.
This is the question you must ask yourself. My service dates are from 1978 to 1988. 1/75th
we, in our day would never address an infantry officer as man. unless we were already close friends and then only outside of the workplace.
This is a different world today

No, dont' make a stink, he might be baiting you... its outside of work... let his unprofessionalism slide, but remember. Give him the stink eye

Outside of work? Like in civilians off post? Or like in a parking lot after work? Details are important. If you live in the same apartment building sort of thing then yeah calling the Lt dude, bro, fuckface ect works. Don’t pretend that an officer rank makes one special outside of work. Now if it is even remotely in the wheel house of the military, on post, the commissary ect then sure make the correction. Hold to the appropriate work relationship as defined by the military.

It's one thing if he does not know and just comes across you out in the world and does that. Totally another if he knows you are an officer and does it. He may be under the mistaken impression that once the duty day ends and the uniforms come off that you and he are just civilians kicking it. That is not the case. The only thing that changes is that he does not have to salute you when you are out of uniform and not on duty. He still has to show the proper courtesy. You are perfectly within rights to light him up for it. Better you do it than if a CSM or Col does it.

Definitely correct him for the sake of upholding the standards. How you do that is a matter of your leadership style. We would have gotten lit up on the spot for stuff like this. Stern discipline ensures a lasting correction that never needs to be repeated.