To clarify, I support a business's right to refuse service to anyone they want. I'm generally a person who wants less government involvement in our lives.
The OP question was why do Christians single gay people out? Why don't they also refuse to serve people who work on Sunday (by choice) - for instance - or a guy who says "Jesus Christ" in vein all of the time, or a guy who gambles and is divorced, or a guy who's known to worship idols, or a guy who doesn't honor his parents, etc?
Why do they single out the gays as the customer of choice to refuse, as if they are the only humans on the planet who sin?
A person comes in, orders a specialty cake, pays for it, comes back and picks it up. How does the baker know what kind of life that person leads? Perhaps that person worships satan but ordered a puppy cake for his kid. A gay couple comes in and orders a wedding cake, it is apparent they are gay. Your question is a bit ridiculous. And say that customer ordered a puppy cake and a devil worship cake ... doesn't the baker have the right to refuse to fill the devil order?
I'm not sure what all the fuss is about over this. A business has the right to refuse to do a job. Don't they? What does the reason matter?
Should a photographer have to take a job photographing tarantulas?
Should a house painter have to take a job painting an awkward house if they don't want to take it?
Should a baker have to bake a specialty cake that is explicit (say a cake for a bachelor/bachelorette party that is genitalia)?
Doesn't a business have the right to turn down work?