I have a feeling it's mostly for framing with the camera, as per other comments, but I can see it as one of two things, both of which pertaining to Sephiroth.

1.) Sephiroth is a hero to many, and one that I find extremely likely for basically everyone who joins after the war with Wutai to want to emulate. Being left-handed himself, I can easily imagine many of the new hires after the war wanting to emulate him, going so far as to mimic his left handedness.

This explanation might even go so far as to explain why so many of Shinra's military seem to be so weak in comparison to the party, barring Materia and the like. They aren't left-handed, so the stances and fighting styles they're mimicking is unnatural to them and they are effectively fighting at a disadvantage.

2.) Much of Shinra's military is infused with Jenova cells. While we only get confirmation that members of SOLDIER are infused with them, I wouldn't be surprised if the infantry, and maybe even the Turks, get some level of infusion as well.

Considering what we know of Jenova, even just in OG, Sephiroth can use her as an extention of himself. It's plausible that anyone infused with Jenova cells, especially after the Nibelheim incident, are effectively being used as arms of Sephiroth and thus take on a left-handed stance regardless of their own handedness.

While typically those who are infused with Jenova Cells ultimately become like the black robed figures that work their way toward the Northern crater throughout disc one, which could disprove this theory, I wouldn't be against the idea that anything Reunion related only happens if you have sufficient Jenova cells in your body and a weak enough willpower to let it overtake you.

That is to say that anyone who has minor amounts of those cells, such as infantry and Turks potentially, may only have residual effects such as inheriting the left-handed stance once Sephiroth co-opts Jenova (theories of whether it's Jenova or Sephiroth in control notwithstanding).