Why is the bandana so popular with russian soldiers?
My guess would be weight. You see many Russian special units without armor and helmets, especially GRU. They cover large distances for extended periods and weight reduction allows for increased agility and ability for hand-to-hand which is given an ample amount of attention in training. Not to mention helmets don't really help even exacerbate the sweat issue.
They have possibility to dress bullet-proof vest and helmet, but they don't put on them. Can be better they know, what do?