So sorry, it is cruel to deny intimacy and it is wrong to be a thankless bitch. Just because you do not share religious belief it does not mean that there should be a denial of affection.
If this situation is unlikely to change how long can you continue to live in this way? Is it better to be alone with the opportunity to find someone who loves you rather than staying with your wife and trying to change a bad situation? If there was no sex but your wife showed affection and appreciation in other ways then there is a reason to be together otherwise you are just two people occupying the same space with no emotional connection.
Everyone needs to feel loved, sex isn't everything but it is important in a marriage.
I would talk to her frankly about how you feel. Ask her if she will agree to counselling. If she won't work with you and doesn't want to change then perhaps you need to rethink your relationship.