Star Fleet would *have* to be the military, if only because in times of war they are the ones out there fighting for the Federation. Whether it's the against the Klingons at Organia or the Dominion at Bajor or the Borg at Wolf 359... that's where there'd be the military, that's when we'd see the major military force of the Federation. And who's doing the fighting? Star Fleet.
It seems the question isn't so much "Is Star Fleet military?". Might as well ask "What else is Star Fleet besides military?"