All things being equal, the Church would prefer that Catholics marry Catholics. Shared religious beliefs and practices are important factors in establishing a closer union with another person. Catholics also see marriage between Catholics as an essential way of passing on the Catholic faith from one generation to the next.
America is, however, a society in which Catholics and people of other religious faiths encounter each other each day. Marriages between Catholics and other Christians are quite common. The Church allows such marriages but asks the Catholic to promise that he or she will do all possible to continue in the practice of the Catholic faith and have any children baptized and raised as Catholics.
If the Catholic Church allows the wedding of Catholics and other Christians, it accepts the reality that Catholics and other Christians in a society such as ours will meet and sometimes want to date. We indeed may be attracted to a person whose life experiences have been different than our own. Hearing more about the religious beliefs of a Protestant Christian may help a Catholic to understand his or her own tradition more deeply. We may be forced to think about aspects of our faith we have always taken for granted.
When a Catholic dates another Christian one important guideline is mutual respect. We should respect the religious beliefs of the other person and what he or she regards as holy. And we should expect a similiar attitude of respect from the person we are dating. It’s wise to avoid arguing about differences in your beliefs or accusing one another of sins your churches may have committed in past history. Instead, your dating relationship might provide an opportunity to learn about each other’s beliefs. You may want to attend each other’s Church on a Sunday and learn what is important to each of you about the tradition to which you belong. If the relationship becomes serious and seems headed toward marriage you may even want to study each other’s beliefs in more depth. Most Catholic churches offer a regular class explaining Catholic belief and practice and other Christian churches have similiar classes to teach about their own traditions.
Your own question was more specific: you mention that the woman you were dating had a very strong faith in her Christian church and did not believe a relationship between her and a Catholic man would work out. She believed that if she kept seeing you, it could become more difficult for her to practice her own faith. As difficult as it is, it’s important to respect her decision. Some persons are able to date or even marry a person of another Church and still remain strong in their own faith. Others cannot. Honoring her feelings and her decision in this matter is part of respecting her faith and the importance it holds for her. Every relationship is unique and personal, and the honest sharing of feelings and values with one another is a key way to determine whether this particular relationship offers a future for both of you.