The issue would be washing new, un prepped cotton with synthetics, whether the synthetics are new or old. The oils can get on the suede cloth and "clog" it up to make it not absorbent, or the cotton can shed and do the same thing. But washing cotton with cotton is never an issue.
That's what I have heard too, just an issue when you prep natural and synthetics together. I throw new ones in with a load of regular wash, unless it's hemp or bamboo. They're the biggest culprits for oils.