Do I have to give up my religion to follow AYP practices?
Not at all. There are many people from different religions who follow AYP practices. Assuming your religion teaches peace and non-harming of others, AYP practices should greatly help with your religion.
Religion means, "to bind back together". Through identification with our body and senses, the illusion that we are separate from the world and everyone else, is created. Yoga provides the means for us to undo this separation by practicing daily techniques.