I think it is a very tough question from a legal standpoint. Should a Jew be able to deny service at a restaurant to a Christian? Should a Protestant be able to refuse service to a Catholic?
In my opinion, anyone should be able to deny service to anyone.
That said, I can understand the position of those who say anyone in the food/lodging must equally serve all who walk through the door; people, as a general rule, have to sleep every day and eat several times a day.
This does not apply to services such as photography, cakes, flowers, and the like for homosexual pretend-weddings. If one provider doesn’t wish to serve them, there is plenty of time to look for alternatives.