Until it can be finished and washed, I use one of the sticky rollers to get the hair off. Works great and doesn't stretch or distort the fabric if I go slow and careful.
But really, I do my best to prevent it in the first place. Knowing my cats will go in my quilt room and curl up on my projects, I often put something equally as soft and comfy on top of my work in progress (like a doubled over piece of flannel that covers the whole project). This works great for me. My project is protected, but all it takes is a quick removal of the flannel when I'm ready to work on it and I'm off and quilting again.