If an enlisted person of one branch comes across an officer of another branch, does he or she have to salute the officer?
Yes.
All officers are to be saluted by all enlisted members of the military, regardless of branch. The regs are somewhat different by branch; for example, Navy personnel don’t salute left-handed or sitting down, but generally speaking, yes, enlisted are required to salute officers.
Foreign officers are also required to be saluted. If a particular base has a population of foreign officers, base personnel are told what to look for.
Thanks.
My dad said he hated the navy because they had so much crap on their uniforms that he was always accidentally saluting enlisted men (he was a marine).
Should be mention that officers are required to return the salute as well.
And in the Navy when you are inside and uncovered you do not salute.
On Marine bases, they even salute cars that have an officer’s sticker on it, regardless of who is driving. Or at least they used to.
Us recruits at Great Lakes saluted every car; cars there either belong to a superior or a civilian and the former is much more likely than the latter.
Recruits salute everything, since, as we were so often told, they are lower than whale shit.
The rule was:
If it moves, salute it.
If it does not move, pick it up.
If you can’t pick it up, paint it.
My dad was in the Navy and he told me the rule of thumb was: “If it moves salute, if it doesn’t, paint it”.
I was not quick enough.
And only when in Uniform.
You also salute any foreign officer.
Only when in complete uniform. I was taught no hat no salute.
What about enemy officers?
Only if you can get away with it and stay alive 
Not in the Army. Officers are perfectly entitled to ignore you completely. If you are walking past them you hold the salute until you pass, if you are stationary you hold the salute indefinitely until they return it, or give you an order.
Proper military etiquett requires it, when you greet one any place but in the middle of a battle.
I recall two instances of how odd this struck enlisted men. One was of a Marine who was ordered to be a member of a salute-firing party on a ship that was burying a the body of a Japanese (offficer) pilot who’d crashed into the deck. He followed the orders, but didn’t fire his weapon during the salute.
Another (from Studs Terkel’s “Good War,” if I recall correctly) was when some Americans captured a group fo Germans that included their chaplain, who was a bishop. The American chaplain (preist) heard of this and made a special trip to visit, not only saluted, but knelt to kiss his ring. Perfect clerical obedience, but the GI’s were pretty disgusted, after what they’d seen of the Germans.