I see it more akin to a Doctor who only performs abortions on black babies and won't perform them for Asians (or pick any combination of races/ethnicities you'd like).
What does race or ethnicity have to do with this case? If your practice relates to family planning/fertility and your personal beliefs (correct beliefs, I might add) are that God’s definition of a family includes a father and mother (male and female), then you should have the right to restrict your practice to said couples.
I have yet to find anywhere in the US Constitution a protections for sexual orientation. Much like so many other prohibitions and “rights”, this was engineered by congress and liberal courts.
Constitutional protection is extended in the case of race, religion (where it does not inhibit the person from performing reasonable expected function), gender (not gender confusion), and ethnicity.
One of the last (apparently) bastions of true Constitutional Conservatism relates to a person’s freedom from government’s heavy hand.
What is next? Doctors will be required to perform “gender re-assignment surgery”?
And I stick to my abortion illustration. If a doctor believes that abortion is wrong, then he should be allowed to refuse to perform them.