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)

First up, I am sure your MIL was well-aware of your religious inclinations before you got married. However, if she feels the need to introduce her religion to your child, it should not be a problem as long as she does not want her to follow that faith. However, if you feel that your MIL is in fact, trying to persuade your girl into following her faith, you must have a heart-to-heart with her keeping your husband in the loop. It's better to let your husband do the talking though, and explain things to his mother directly. Both of you can be the voice of reason since it's a sensitive matter. You are the best judge of how your child should be raised and therefore, sharing this with your MIL at the onset would be better than regretting being silent later. The best part, if you allow your child to follow both faiths, she will get the best of both worlds.