I have always made it a habit to wash fabric before cutting, with the exception of pre-cuts. I wait until the quilting and binding are done before the first wash. I agree with those that suggested hand washing the top and backing and then line drying as it will avoid any dramatic shrinkage and unraveling. If the top and backing must be machine dried (for those in colder climates), I would suggest sewing a seam as close to the edge as possible before washing and machine drying to help minimize unraveling.

I would love to have an outside clothes line, I grew up with one, I had one until... you guessed! it I moved into the condo lifestyle. So many single family communities don't allow them, especially on Sunday's. I did read an article many months ago where people were working to bring it back into vogue, using the arguement it is better for the environment.
I will cheat and throw my bathroom rugs outside over the fencing to dry, haven't heard any complaints...yet.