This is NOT just about sexual orientation, people are assuming it is and that is indeed a part of it, but it is about so much more. It is about the rights to practice what you believe.
And being white or black isn't a religion, so no they shouldn't have that right. And I have known many businesses who do stick strictly to what they believe in and you know what, they are usually the most successful businesses.
For example, we have a car dealership out here in California that was bought by a Christian Family and they decided that they were going to close on Sunday (something that in some parts of the country is illegal for a car dealership to do by the way). Prior to them buying the dealership, Sundays were the busiest sales day for this dealership. The city even tried to stop them from closing on Sundays, luckily our laws didn't allow them to do that. And you know what happened? Their sales were double what they were the previous year (oh and they bought the dealership after a really good year) and have increased every year since then, even during the economic downturn. They stuck to their religious beliefs, despite being persecuted by the city, etc. and it has paid off for them.
Now what would have happened if they were in one of the areas that is able to prevent them from closing on Sunday. They would have either had to remain open on Sunday, against their religious beliefs or risk jail time.
The same thing can be said about morning after pills, same sex marriage, abortion and a number of other issues. This is about protecting the freedoms of everyone, no matter what their religious views are.
You picked a really ridiculous analogy. Not serving on a Sunday is not the same as not selling to a particular group of people.
Being white is a religion for some and it was law up until not so long ago that black people had to stand on the bus and would not get served in particular places.
This is about sexual orientation. If it was about beliefs, this law wouldn't get even mentioned as the right to refuse admission is already lawful and covers any business owners right to refuse. It's just that now they can say they can refuse you because you are gay without being attacked by the media.