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

Spot correct "to the level of the situation". So an "off duty" error starts with an immediate, polite and "quiet" reminder of rank and decorum.
Why?
Let me put it into the way it was presented to me:

I joined the unit softball team, that was mostly various enlisteds but had a at least one Officer, the third baseman...
Even though he was from another portion of our unit, I was told to "sear" his look into my mind (since he'd never have his rank on "during the softball activities", and ALWAYS treat him like an Officer, no matter what the "team" situation was. Because maybe, one day, I could have to do something with his part of the unit.
And if I were to "slip up", heck would be paid...
but then again, even being 100% professional "on duty", if someone were to see us "buddy buddy" on the team, and if during our on-duty interactions the mere "hint" of "me getting off easy" came up, HE would be the one to "pay the heck" that comes out of the "favoritism".

There is no room for disrespecting on or off duty. It's a 24/7 requirement 365/6 days a year. If you didn't you request the greeting, then I would correct the unpleasure gesture greeting.

Were either of you in uniform at the time? Remember, it's your rank they salute.

It sounds like a discipline and respect training area. You should confront the soldier, get his unit and 1SG name then report to his unit the incident. I had a similar incident at a High School where a student (HS junior) call his counselor (female) DUDE. MMM this did not go over to good with me, as I waited for the student to leave the room, them I questioned the counselor if I heard right. Today, discipline and respect is taught at the home, but with the corrupt world we are in now, this is not a priority for families, especially when they are mostly single moms or dads.

Of course!! Also, make sure they are saluting you… it’s crazy how slacking our military is on respect and responsibility. All I see are overweight, lazy, soldiers.

I can tell you the "sir" thing is just a formality. Think of it as a slow clap. I remember seeing recently out-of-the-joint Yardbirds calling our ChEng Mickey and he wanted to be called Sir rather than ChEng or LT. Hey, hey you, or yo is just rude.

To maintain the sanctity of customs and courtesies and the profession of arms, the short answer is yes. But, how you do it is what he or she will take away from it. Use the opportunity as a teaching moment and treat the soldier with dignity while you correct the behavior. I’ve see peers berate subordinates when it wasn’t warranted, and it not only didn’t fix the problem, it created a lack of trust and respect for the senior leader.

Customs and courtesies. As an Officer, you set the standard, or lack of a standard. As an O-3E, I would always make OTS corrections. It speaks volumes!

Jack his Boots.

Teaching moment for you to train him and then let his senior enlisted know