Yes, I consider Starfleet to be quasi-military. There are certainly branches (like the MACOs) whose primary purpose is military...
The MACOs were not part of Earth Starfleet at all. The Earth Starfleet seen in ENT was explicitly a non-military organization (despite its use of military ranks -- kind of a conceptual glitch there), and so needed to team up with the actual military, the MACOs, when a wartime situation arose. But that has no bearing on the status of the
Federation Starfleet, which obviously is the primary (and seemingly exclusive) military organization of the UFP.
but the exploration branch doesn't really fit into a neat military definition, since the crew spend most of their time functioning as scientists, aid workers, explorers, and diplomats (wagon train to the stars doesn't conjure a view of a military organisation) and security staff seem to function more like police officers and bodyguards rather than soldiers.
As I already said, those things
are, or at least can be, included in the definition of a military. No nation is at war 100 percent of the time, so a military cannot be assumed to exist exclusively for combat purposes. Again, don't confuse "military" with "militant." There are plenty of scientists, engineers, aid workers, and explorers within the armed forces of the United States. Yes, Starfleet's priorities are more heavily shifted toward such activities than those of our military, but it's a matter of degree, not type.
In times of war the ships do function like a navy, in TWoK the civilian scientists viewed Starfleet as military, and in NuTrek they've been defined as a 'peacekeeping armada' (is it just me or does that sound creepy?).
Further: In "Errand of Mercy," Kirk told the Organians, "I'm a soldier, not a diplomat." Interestingly, not long thereafter in "Metamorphosis," McCoy told Kirk, "Maybe you're a soldier so often that you forget you're also trained to be a diplomat." In "Obsession," Kirk asks Ensign Garrovick for his "military appraisal of the techniques used against the creature."
Then there's this exchange from "Whom Gods Destroy":
GARTH: You, Captain, are second only to me as the finest military commander in the galaxy.
KIRK: That's very flattering. I am primarily an explorer now, Captain Garth.
GARTH: And so have I been. I have charted more new worlds than any man in history.
There's no question that Kirk considered himself a military man first, an explorer second, and a diplomat a distant third. He was modeled on Horatio Hornblower, after all. Picard considered himself an explorer first, a diplomat second, and a military man a very distant third or not at all, but he still belonged to an organization that had the structure and function of a military and that bore the primary responsibility for the Federation's defense. Any armed organization charged by the state for its defense against external threats is, by definition, its military, no matter how infrequently it actually participates in war or combat.
Again, I come back to the point: what should they do to demonstrate equality on screen?
The best they can. I don't think it should be a matter of mere quotas, although it certainly wouldn't hurt to see the occasional female-majority bridge crew to balance out all the male-majority ones. (For what it's worth, the current bridge crew/senior staff on the
Enterprise-E in the post-
Nemesis novels published by Pocket Books is predominantly female; Picard, Worf, and Geordi are pretty much the only male core characters left, though there are several male supporting characters as well. This was not an intentional choice, but just something that happened as assorted authors -- myself included -- decided independently to add new female characters to the cast.)