[Old Sarge]

do folks in one branch of service have to salute folks in another branch if their rank is higher

Yes - if it's a salute zone.

Here where I am, we only salute when a two-star general or higher is visiting.

And if the Commander-in-Chief ever appears? Who knows!

[Army Air Corps]

An uncle once told me that all he remembered from basic training was "If it moves, salute it; if it doesn't move, paint it".