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

Grab the nearest NCO and have a smoke session. Heh.

Of course! It's your duty!

It troubles me that you're an "officer" (a captain) and feel a need to ask this question! I might be a little more understand if you were a fresh butterbar!

Well I guess that all this doesn't matter now since the snowflake "woksters" want "Sir" and "Ma'am" removed from the military vocabulary. By their standards " hey you, hey man," and even a " hey fuckface" would be perfectly acceptable..... until the demands for dentures start to overwhelm the needs for political correctness.

Short answer - Yes.
The standard that you walk past has become the new standard. If you accept "hey", will you later accept "yo"?
Even when not in uniform, a Soldier is a Soldier.

Yes, he should be corrected, but how it's done is up to you.

Yes!

quite frankly if you need to ask this question you should not be an officer no hard feelings Jeff R

Really? In today's military culture you want respect? Straighten out your puppy mask, polish your fingernails, get your shorts on for guard duty, trim your beard and shine up your stress card. There are no standards any more.

When I was in BASIC TRAINING yes SIR no SIR yes SGT no SGT was pounded into us. Even when I got to my unit if I would mess that up I was corrected on the spot
This is simply second nature