Straw and rabbit poop will compliment each other in the compost pile, straw is the carbon component and the poop is the nitrogen. There are recommendations as to the proper percentages (70% carbon, 30% nitrogen if I recall correctly?) but I just pile everything from the property in the compost bins and it breaks down just fine. I have six compost bins about 48" cubed and they take dirty bedding (straw, shavings), chicken, duck, rabbit and turkey poop, butchering offal, kitchen scraps, dead animals, grass clippings and other yard debris, it all comes out as a nice black compost. it's about a two year process for each bin. My point is that everything organic will break down in a compost bin just fine over time.
My rabbits have been on straw bedding out in the colony for a few years now. Whenever I change the bedding out they will munch on the fresh stuff for a while. They have their general pee corner which needs to be cleaned out a bit more often but I find the poop pellets work their way down through the straw as the rabbits hop around on it so it keeps them pretty clean and not in much contact with it.