Can I dye cotton curtains in my washing machine?

I bought these lightweight red cotton curtains 4 years ago. They have faded dramatically in the sun, and are now a strange orange-yellow color. I bought some red RIT dye, and am wondering if I can just throw it all in the washing machine. If so, what about my next load of laundry--is there any chance it will end up pink?? Just want to make sure I'm not going to mess up the washer, and/or accidentally stain the next load of laundry.