RE: Should a Privately-Owned Business Be Able To Refuse Providing a Service To a Customer?

You have never owned a business, obviously.  The owner of a PRIVATE business doesn’t HAVE to do anything.  It’s not our place, as society, to force him.  If you don’t like what he/she does, don’t patron the establishment. 
For instance, I don’t shop at AutoZone, Starbucks, Wal Mart.  I don’t buy anything made by Nike or watch films by people who despise me because I wish to produce a product and service of value and sell it to those who are willing and able to buy it.  Through the unforced judgment of those who wish to deal with me, and I them. 
If I don’t want to buy their product, I won’t.  If I don’t want to sell them my product, I won’t.  That’s called freedom, and liberty. 
If you think it’s acceptable to force someone to do something, go be forced.  Those who advocate slavery should try it first.