Jaba -- I have three cats. I washed, dried, cut and bagged the fabric in one time block. The cats were no where around during this process but do whatever you have to do to my fat eighth to stop an allergy attack before it starts. I routinely clean my cutting area prior to using it but one never knows if a stray cat hair is waiting for me to turn my back.
Congrats on the new grandchild!! Such an exciting time for you and your family.