One should be able to determine who one does business with. I just wish they would post it in the window or on their website so as to not waste people's time and I can avoid doing business with them also.
One of my biggest complaints about these business owners is that they hide their views and then spring them on would-be clients instead of being honest in their advertising. Two cases that I actually checked on were that crazy baker in Colorado and a wedding venue. They never said a word on their websites that they would refuse business. Instead, the message to the public was "come to my business." I do, however, support public-accommodation laws that are generally applicable to all business owners.
I also have a question as to whether these business owners would be in favor of all business owners having the right to refuse service on other grounds, such as religion. Would an LGBT business owner have the right to refuse service to someone who is a member of an anti-gay religion? Everyone should have the same rights.