Urine is sterile when it comes out, but the dead cells and whatnot in it can lead to bacterial growth when allowed to sit and, ahem..."ferment". 

I have never used a pee rag -- to be honest, I had never even heard of the concept! Fascinating way to reduce environmental impact. I'd suspect using a synthetic microfiber cloth would be preferable to a natural textile...easier to clean, easier to dry quickly.