Can Christian women touch the bible when they are on the cycle, since Jewish and Islamic women can't?

Christianity doesn't consider women to be unclean. It doesn't consider the human body to be unclean and it doesn't consider human reproducation to be unclean. So the answer to your question is yes women can touch the bible when they're on their period, and no christianity does not consider any part of the menstrual cycle to be unclean.