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)

This is tricky but it has to be handled sensitively especially since it concerns religion. Ask your husband for help in talking to her but don't make her feel ambushed. Since you both agreed early on not to pressure each other, then I think he should help. By the way, I wonder how old is your daughter? Perhaps when she's older she can be the one to decide what religious practices she's most comfortable with.