On a brewday I quickly rinse out my BIAB and also any muslin bags/cloths as I use them and pop them into the washing machine, the quick rinse takes most of the bits off. At the end of the brewday our washing machine has a handy rinse/spin cycle which takes about 20 minutes and gives all my grubby cloths a good rinse and spin without using any detergent. They come out very clean, almost white and I pop them on the line to dry for a couple of hours.
Any muslin cloths you are using but not in the boil, ie. for dry hopping or sieving through should be boiled in water for 15 mins to sterilise just before using. Any muslin cloths being used in a brewday boil don't need to be sterilised as the boil will take care of any bugs.