The ones in the ST:FC "standard" uniform were Lieutenant Larkin, Crewman Kellin and the reinforcements that arrived at the end. All the fighters in the trenches wore either the special fatigues with the strange padding and the chest stripe, or then t-shirts, or other nonstandard uniforms apparently improvised from those.
We might draw two opposite conclusions here:
a) Only Larkin and Kellin and the reinforcements were Starfleet, the rest were Marines or Army or somesuch, and the uniforms reflected that.
b) Only the commander of the outfit bothered to wear full regalia out in the field; the rest of the Starfleet force had "let their hair down", save of course for Kellin who had a nice indoors job.
I rather favor the latter interpretation, because there is no indication that the reinforcements would have been from a different service than the originals. Indeed, it is a drama point that the nicely clad newcomers will soon grow up to be the exact same as them gruffy and grimy vets.
As for TOS, the redshirts were the Marines in every practical respect. They just didn't happen to wear camo - just like today's Marines don't wear
this. Probably the development of warfare has outdated camouflage, much like it has outdated the use of standards and bugles.
A trio of redshirts (like in "Obsession") would pack far more firepower than a squad of USMC troopers could hope to haul or bring to bear. Essentially, they'd be carrying three 20mm autocannon with essentially unlimited ammo, at least one radar and IR set, three long range radios, and what amounted to a lightspeed-fast personal helicopter for each. Thanks to this, they could plausibly omit things such as grenades, canteens, maps or tents. Whether the omission of protective gear such as helmets or breast armor were plausible would depend a lot on the mechanisms of 23rd century warfare.
Timo Saloniemi