For outside, for better appearance sake i have brown handkerchiefs, cotton, and i find they wash just fine with other coloured laundry, but they’re less absorbent than my next 2 choices.
But at home, i use brown cotton teatowels ( less than a tenner on well known site beginning with A for 6), and any colour microfibre cloths ( lovely and soft, similar price same site). Again, they wash just fine with coloured laundry in the machine.