Of course! Just like a Church that has snake handling as part of their belief may deny marriage ceremonies that do not include the bride and groom handling snakes. Can a church refuse to marry couples of a mixed religion? Sure. They do it all the time. Same race, different race, makes no difference. A mosque will not marry a believer and an infidel.So if churches should be allowed refuse to marry homosexuals couples, should they be allowed to refuse to marry mixed race couples if it goes against their doctrine?
I can't think of a religious organization that has a religious belief in not marrying mixed race couples. Can you name one? If there was one, then yes they should be able to deny marriage ceremonies to mixed race couples.