Anything Wrong With using Polymer-Coated Steel Case Ammo in Guns ?

I know we all like to stock up on ammo best we can, also stay in practice with our weapons. As I am always looking for the best deals on ammo, I keep running across these Russian polymer-coated steel case ammo. Of course in my Mosin-Nagant, I buy this without second thought, I figured it was what it was made to use, but in my other guns I am honestly, quite leary. Now this ammo is non-corrosive, but still I have a hang up with steel case ammo even if it is polymer coated.
I am not going to claim I have the best weapons money can buy, but I think I have good quality weapons, and I don't want to do damage to them trying to save a few dollars on ammo. Is this steel case ammo ok to fire in these weapons?, or would a person be causing undue wear on weapons designed to handle brass-cased ammo? Anyone have an opinion, I'd like to read it, thanks. -dave-