Looking back on my formative years, I have noticed that influential people in my life tended to present things as very black and white, and as an adult I now realize that things aren't that simple. For instance, it took me quite some time to understand drinking in an of itself is not a sin.
Similarly, becoming romantically involved with someone who doesn't share your faith is perhaps inadvisable, but not a sin. What comes to mind for me is 1 Corinthians 10:23: 23 “I have the right to do anything,” you say—but not everything is beneficial. “I have the right to do anything”—but not everything is constructive. In other words, though it is not forbidden, it may not be particularly wise either. Two mismatch worldviews may cause more tension, and it seems like it might take a lot more work to keep the relationship going.
The question of shared faith seems to permeate so much of a relationship, especially when you're talking about holidays, child rearing, what to do with your money, and so on.
In some ways, I wish this weren't the case. It would certainly increase my relationship options if I weren't holding out for someone who shares my faith. It is something I still struggle with, especially when I meet people of different faiths (or no faith) with whom I get along very well. I start to wonder if the mismatched faith thing is really such a big deal.
In the short term, I am not sure that it is a big deal. Dating someone who does not share my faith may not have quite as many implications as marrying and having children with that person. So sometimes the only thing that gets me through is looking at the big picture.