How does religion affect the relationship between Romeo and Juliet?

Readers are likely to assume that Romeo and Juliet are practicing Catholics. We don't get to see them at a Catholic mass or anything like that, but Romeo's close relationship with Friar Lawrence is good supporting evidence that Romeo is religious. The ease with which both Romeo and Juliet weave religious images and references in their conversations with each other about how much they love each other also indicates that they are practicing Catholics as well. The first way that religion affects their relationship is in how they use religion to emphasize how much the other person means to them. For example, there is the following line from act 2, scene 2.

Call me but love, and I’ll be new baptized.

Romeo is asking Juliet to call him her love, and he says he'll be baptized anew. Some readers interpret this as Romeo saying that he'll take on a new name, but the baptism aspect of it makes it so much deeper. Baptism is a sign of God's covenant with believers. A baptized individual does take on a new name in Christ and agrees to live out life in a certain way as thanks. For Romeo to use that kind of language shows just how deep his commitment is to Juliet. Romeo uses his religion as a way to emphasize his love to Juliet.
Another way that religion affects the relationship is in the fact that Romeo and Juliet get married before having sex. This marital precedent of remaining chaste until marriage is a direct result of what Romeo and Juliet would have learned as Catholics.