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

yes sir you correct him tell him to get down and do push ups until he corrects himself
you have earned the respect lead by example

jcv
1st 75th c co wpns plt

This is a “no brainer”. Definitely and put him in his place in front of his peers if possible to prevent others from duplicating his remarks. Be careful though to ensure you come off correctly and not a over eager because of your rank. It’s about respect

Are you in uniform? If not, why bother correcting him?

well, formal wise he us wrong and you can correct that, but if you need to decide if it is because he is really friendly and is giving you a shout out be kind on the redressing of how you wish to be addressed. I was an E-5 Corpsman and my duties were called Public Health Office, I went to the Ward Room and Offices calls as well supervised teaching and drills of medica personal in the Sub Squadron,, I was addressed as Mr. by most Officers and called them sir. When with them alone I called them by their first name because they said I could.

As long as he shows respect for the rank on duty,I’d let it go.

Correct that SPC!

There was a Cpt. I saluted while walking on post and he returned the salute left-handed. I would say something, the SPC needs to respect the uniform regardless.

You’re either an officer or one of the boys. Choose carefully here

You're a CPT, and are wondering if you should be correcting a deficiency in military bearing? Allowing it to continue will only encourage further breaches of decorum, extending to him not even acknowledging your rank at work.

Tell you what: find a full-bird you don't "directly work with" but "come across a couple times" in the course of your work. When you next see them in civvies, say, "Hey, man. . ." See how long it takes for your face to be removed.

Hey man, maybe there’s a bigger issue than how the SPC addresses you.