Sure they would. You advertise you make wedding cakes, you're going to get all faiths, races, creeds, etc. You can't refuse service to any of those and there IS biblical justification for all of it if you look.
Race and sexual orientation are both immutable traits...but it's the bigots and the discrimination that are actually being compared.
The Christians follow the New Testament, not the Old Testament. The Old Testament is a historical reference of what Jesus came to set straight. Jude 1 is in the New Testament. It forbids the promotion of any homosexual culture. Marriage is the core of any culture. Ergo, gay marriage will get you eternity in the slammer. Not just 10 Hail Marys or counting your rosary beads after confession on Saturday. It's one of the major sins a Christian can commit.
Anne Heche tells us that sexual orientation is not an immutable trait. The fact that lesbians have children naturally means that sexual orientation is not an immutable trait. The fact that most gay men have been molested as boys means that homosexuality most certainly is not an innate trait.
Now if you want to discuss how homosexuality is a stubborn mental habituation, then yeah, we can go there. Look at the data (and the sources, Clinical Psychiatrists, the CDC and the Mayo Clinic..]