First of all, both sentences, as stated by Giles, are equivalent. If you have a problem with “I have a Christian father,” I don’t see how you don’t have a problem with “My father is Christian.” What’s the difference?
Second, why are you limiting this to religion? Or are you? Do you have the same problem with someone saying “My parents are European” vs. “I have European parents”? The precision is just as low, if not lower, in that statement.
Third, often, that level of precision is simply not necessary. If its not germane to the conversation what particular flavor of Christian your father is, why include that information?