It is worth of note that who to salute isn't likely the same everywhere. Locally, there's a few people and things in specific that servicemen need to "honour" (when alone, snap into attention and salute/when in formation, command attention or parade: heads of state, national flags and funeral processions to name the most obvious), but when in uniform, a salute is the default greeting of a soldier. Similarly on speaking, locally we don't have the ridiculous "sir yes sir" culture, the superior officer is addressed by his title once in the beginning of the conversation and that's it.
For Amarr, the military would hold a strict system of ranks due to obvious reasons, but Holders and high-ranking clergy would likely be the object of the Amarr equivalent of a salute. It is noteworthy that they do have a class society, as hinted by some Ammatar news: A dirt-poor Holder is still strictly above a commoner who's rich enough to buy a few planets. Several Imperial bureaucrats might be saluted, as well, though most would be already clergy or Holders by their own right.
For Caldari, I assume that there's the default corporate structure, so people above you in the chain of command would be saluted, plus possibly superior officers of the corporate security in general (would have to check the fiction on this). For some more martial-oriented corporations (KK, Minedrill etc.), this might be extended to the entire corporation. If this is the matter, there's likely a cutoff at some point, however, so a rank-and-file security guard wouldn't salute a production line supervisor from another colony (except possibly when in that colony) but would salute the general manager of that colony visiting the guard's colony. We do, however, need to take account the identification of these people. Military (when not in combat) carries usually visible markings of their rank, but unless a similar rank system is implemented for civilians (work dress), enforcing salutes is not possible. Of course, it is highly possible that several corporations do have corporate-issue work clothes, so seeing someone dressed like a Hyasyoda personnel manager a Corporate Police Force officer would immediately know that saluting was in order.
For Gallente, I'd expect things to depend a lot on culture, as well. Culturally important figures might get saluted, even if the Federal Military Code directly wouldn't enforce it. Some members might have their own (para)military ground forces, but like the Amarr. The Intaki system, however, is the only attested case of a member-state having their "own" navy, in this case the Mordus' Legion Command. The paramilitaries and state militaries do not necessarily follow Federal code. However, I'd assume that the President as well as high leaders of the democratic instutions are saluted. (Can't remember off the bat, but there are likely countries where the Speaker of the Parliament is the Head of State - as a historical example, I think the USA was one before establishing the office of the President. In my native country, the Speaker comes before the Prime Minister in official protocol.)
Minmatar tribes might have their own customs. A lot depends on the old Minmatar culture and its current reconstruction. They might have a Gallente-style military, and on top of that special salutes used in tribal events, such as meeting your chief. To compare with the Amarr, certain high clergy in Amarr might receive a special salute or blessing from everyone below him (or her) in status, and for Minmatar the tribal chiefs and shamans might get a special greeting from the members of their tribe. Some of this might be used everyday, whereas some of it might be only preserved in ceremonies.