The rifle shooters wear stiff clothing, while pistol shooters tend to wear looser things (and there are lots of rules around clothes not being allowed to provide support).
Meanwhile in rifle it's all $2k kit of rigid jacket and pants. If you aren't using the rigid jacket and pants, you will get absolutely wrecked. Your score will be lower, and your back will get injured in the long run because of the contortionist posting when holding the 13 pound rifle up for hours. It's not possible to be competitive without it.
First one I thought of proves you wrong? https://www.npr.org/2024/07/31/g-s1-14616/olympics-paris-sha...
Though in that specific case, I'm pretty sure she's got part of the hand in the pocket, and that shooter Kim Yeji also does hand in pocket other times, if you've seen her at other issf events (here's a random example):
https://old.reddit.com/r/olympics/comments/1eheidc/olympic_p...
I've also done finger through belt loop, it's basically the same thing. (Guess it wasn't technically a belt loop, but like a utility holder loop, like you'd put a small hammer in on the side of work pants?)
Sure you can find a few that don't, but that's real missing the point.