Chamois are great. I've used them for about 15 yrs and they work perfectly. The key is: make sure they are 100% sheep skin. There are many synthetic chamois available. These work okay for a short period of time, but wear out quickly and leave "debris" on your car as they breakdown. IMHO, they have to be 100% real sheepskin.
A "real" chamois" can be cleaned, evan of grease and oil. Just toss them in the washer w/ a mild liquid detergent and air dry. They will be good as new. The grease/oil will stain them, but will not effect their performance and will not transfer to the car. Also, I've noticed no problems w/ them harming or effecting the wax.
I've had the same 2 chamois for about 10 yrs. They've gone thru many cars and many wash cycles w/ no problems. They do have a few holes worn in them.
When I bought my first vette, I discovered the "Absorber". Its great and I love it. The only difference between the two is the "Absorber" is more efficient than a chamois. It can soak up more water. I now use the "Absorber" exclusively on the bodies of my cars, and reserve the chamois for the wheels, tires, and engine compartment.
I would recommend both. The "Absorber" may be a little more expensive, but both work equally well IMO.