I just recently watched a video of the origin of various striped white shirts and their evolution. Nowadays the piece of clothing is mostly only used by the Russian military and called Telnyashka. The shirt has a lot of symbolism and is probably as wanted as the Flecktarn or Tiger Stripes are.
The shirt is widely spread for it was in Russian use all the way from the times of tsar Alexander II and had and has been in use by many other before and since. It wouldn't be in any way immersion breaking to see it worn by the Insurgents for example. The Security doesn't really have colorful or non-jacket torso garments so Insurgents will probably be a better fit.
I would hope the Telnyashka to come in all of it's colors: navy and sky blue, black, red, orange and green. Also different styles could be examined but in the case you only want to add one, the long-sleeved would be the best in my opinion.