My husband and I both practices different religion but we made it clear that we will not influence each other. Recently, my MIL wants my kid to be involve in their religious ritual which I am not keen for my daughter to. How can I reject her without offending or hurting my MIL? (as a respect, not mentioning any of the religion)

I guess it would be easier to have both yourself and your husband sit down and talk to your mother-in-law about it as politely, as it can be a rather sensitive issue to deal with. Explain to her that you wouldn't want to enforce any of the religions or its rituals on your child at the moment. You would like her to grow up and make her own decisions.