But they've never de-emphasized the military aspects.
Yes they have. To be sure:
- Junior officers do not salute their superiors
- Fraternization with junior officers is no longer forbidden
- Disobeying direct orders is no longer an automatically jailable offense (sometimes they even promote you for that)
- The inclusion of civilians and/or families on board starships
- The lack of advanced weapons training for officers not specifically assigned to security
- The lack of body armor, heavy weapons, or specialized combat vehicles for ground deployment
- The dual-purpose nature of just about everything Starfleet makes (your tricorder can be used as an ECM pod, your phaser can be used as a forcefield generator, your main deflector dish can be used to cause the entire population of Delta IV to achieve simultaneous orgasm).
- ETA: "desertion" is evidently not even a thing anymore, since Starfleet officers are seen to desert their posts something like four times a season without being prosecuted for it; I don't believe modern militaries take an officer going AWOL so lightly.
And at every turn, they emphasize the fleet's scientific and engineering readiness, which only makes sense, because their scientific acumen is usually ALOT more useful than their combat skills (such as they are), particularly when dealing with a deadly but non-military threat.
Beyond saying they aren't the "military" they pretty much act like the military.
They pretty much act like a bunch of first responders who also happen to be armed with guns and PhDs.
Which is why the description remains accurate:
Starfleet is not a military organization, it is a scientific research and diplomatic body. Although some of its duties include military missions, the purpose of the Enterprise -- as with ALL Starfleet vessels -- is to expand the body of human knowledge.