I am going to call this out as nonsense. Did you watch TOS? Since when is a freakin beehive a "military hairdo"?
No, the beehive (worn by many of the women crewmembers, notably Janice Rand) was not a military hairdo.
But I did say Starfleet was `semi-militaristic`, which means that for the most part they DO follow many of the trappings of the military: chain of command, uniforms & ranks, discipline, duty, and so on.
And often you would have many of the characters discussing these in a given episode: Kirk scolding Scotty and other crewmen for barroom brawling in THE Trouble with Tribbles, Pike lamenting the pressures of command in the Cage, Kirk telling Spock he is unworthy of his uniform in This side of Paradise, Duty and the pressures of same in Court Martial
Where it got to the SEMI-militaristic part, meaning deviations from what was then 1960's strict military code and uniforms came from a little thing unique to television, called ''ART DIRECTION''!
The men on Star Trek all had short clean-cut hair, not AS short as a crew cut but believable enough, and didn't lock the actors into hair styles that might bug them. I'm sure their pointy sideburns were all designed to reflect a more futuristic look.
Where Chekov and Janice Rand (and most of the women crewmembers) deviated came about AGAIN because of a chosen art direction, and the need to appeal and attract a target audience.
Chekov's hairstyle was to bring in a younger female teen demographic, and the women's hairstyle (as well as their very short skirts) was to help bring in horny males!
Sure, the women's beehive hairstyles don`t reflect 1960's military grooming standards. Nor today's for that matter, but that was the point! You'll notice at least two instances I can think of where a female crewmember is shown with her ''starfleet'' hairdo, then later on in a more relaxed look (Saavik in The Wrath of Khan, meeting Kirk in the elevator: ''it's still regulation, sir'', and Lt. McGivers in Space Seed)
Beards and mustaches were also out of the question at that time you"ll notice. Scotty's mustache in TMP was probably agreed upon because the actor refused to shave it off. The first instance of beards I can remember in ST was Kyle and Capt. Terrell in Wrath of Khan. On TNG first season Worf's hair was very short at that time though they grew it a few seasons later. The same with Riker's beard.
All were mandated as changes in the art direction!
But back to what I actually meant: Secret voyage is a non-paying fan film, I get that. We cast the actors we can get.
I eventually stopped thinking of the 3 actors and their different hairstyles, but it was the same as when I watched Starship Farragut's first episode (the Captaincy) many months ago. As soon as I saw the very overweight Klingons, they were all that I could think of, and I stopped paying attention to the story.
Yes I have watched a lot of TOS, thank you very much.