Why does it need to breathe?
Thanks!
Keeping the meat in a breathable bag will allow excess moisture to evaporate and/or wick away from the meat; otherwise it can pool up and become more slimey.
The muley I killed this year after butchering we put each quarter in a cotton game bag and put those cotton wrapped quarters/pieces into the fridge in tubs, going on to debone a quarter a day for the next 4 days. We got very good results from this. I even used a clean cotton t shirt to wrap up the whole neck roast to store in the cooler then fridge and that stayed in great shape that way.