Hint: It's still regulation, Admiral.
I gather that the ban on beards in the U.S. Navy started three years before Riker grew his. So give it time.
Here's one:
The TMP uniforms are more "militaristic" than the TWOK ones. Yes, there are some "far out" 70's tunics that we see on background characters (I think Sulu might wear one at one point when Kirk first appears on the bridge) but all the ones that we see front and center are all navy grays and whites with classic braid (in both the military AND Star Trek sense) and creases. The short sleeves Kirk and Sulu wear look like Navy Summer uniforms (and are THE coolest uniforms in ALL OF STAR TREK). And if the much lauded Admiral uniform doesn't look like military spit and polish then I don't know what does.
TWOK doesn't look like any contemporary military (even if Meyer tried to shoehorn some into it in The Undiscovered Country because - BAD GUYS). They get lightly compared to Napoleonic era uniforms but not in any specifics, just that they're big and heavy. They get compared to Canadian mounties a lot. That's closer to the military I suppose. But there's a much better argument that the Royal Canadian Mounted Police are not a military than there is that Starfleet isn't one.
Might be that UK rules differed so apologies for a) not stating clearly that was where my point originated and also b) for being wrong