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

always correct,
always educate,
always make sure the member is wearing his uniform Properly , it truly starts with how the member wears his or her uniform, if there pride in his uniform appearance there pride in his work , there pride in service pride in customs and courtesies.

Sir,
Yes. Be firm, fair, and final. There really isn't a discussion to be had here. This kind of rot of discipline cannot be allowed to set it. You may be in command of Soldiers like this one day. You may have to send them to die. Something as minor as "hey man" can easily turn into mutiny when the chips are down.

It should remain as I experienced many years ago (Viet Nam Era); not one of us would even have considered such disrespect.

Yes.... Even if you're cool with it, he will run into other Officers who aren't. Somebody will grill him sooner or later for it.

When I was in, you always stopped and corrected them as it was disrespectfully to the rank. You should stop them and correct them. I've been out of the military for 23 years and I still give respect where respect is do even if the person behind the rank doesn't deserve it. Just my 2 cents but that would never have went un-corrected.

You should immediately correct him, I retired as a Petty Officer First Class and I had many officers who I had close relationships with, and only once did I ever address them by other than their rank and last name. In that instance, I called him by his first name as CNO was on the line for him and I could not get his attention otherwise. It is with respect that we address fellow service members by their rank and/or title.

Absolutely it’s common courtesy.

As an officer, or any rank, I would address this immediately. Officers of all ranks are quite easily addressed as sir or ma'am. Although some exceptions apply. I learned that Army chief warrant officers are addressed as "chief". In the Marines, warrant officers are often addressed by their nickname "gunner" (long story).

Enlisted, you can be on a first-name basis with... as long as you use first names, like "chief", "corporal", "sergeant major", etc.

This is *not a regular job*, sir. You are on 24x7, and you're a captain in the U.S. Army 24x7. So is the soldier in question.

This same thing applies to officers. You never, ever, speak to enlisted this way, either. It opens the door.

I retired over 20 years ago. Such a question would not even have been asked back then. There is a different mindset, apparently, in our military today. Is fraternization still a UCMJ violation? Is there still a UCMJ?

Absolutely. I have been informed that the "School of The Soldier" is no longer utilized. That's too bad. It provided meaningful correction without the damage of a written reprimand or Article 15. It never failed to to get the recalcitrant soldier's attention.