No. Freedom of exercise of religion, being in the Constitution, trumps Federal law. Churches can, and do, discriminate against many of the prohibited classes.
Until recently, the general rule was "You can hate ni**ers, or b*tches, or sp*cs, or f*ggots as much as you like in your church, but when you enter into the stream of commerce, you must live by the rules of commerce."
That may be changing. The Bigot Baker case was inconclusive.
It'll be interesting to see if the Red Hen survives the usual tools of the White Right (arson, vandalism, murder, terrorism). It's pretty deep in "paddle faster, I hear banjos" country.