Relationship is fine, however...

Having a general relationship is fine with whomever you like. The true problem one may run into is marriage, when one has to decide on the vows, and what direction the marriage will take. For example, a Pagan and a Christian may happily date for as long as they wish, however, some views may get in the way, such as the Christian vow of "Till death do us part," whereas some Pagans may believe "Till death do bind us forever." This is just one aspect of many differences that religions may have, because marriage is (supposed to be) a permanent step in one's life.

Further, what about the future? Perhaps children? If so, by what religion will they be raised?

In the end, a relationship is fine with whomever, but when it comes to marriage, one must rise, and the other fall, and be reborn, for in marriage there is supposed to be unity, and both must be in step together, towards the same direction, side by side, hand in hand.