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.
The thing is these people don't want to deny point of sale transactions, or non-customized items, they just don't want to perform one contracted transaction, and even if "sprung" on people, it's not like finding another baker/photographer/florist is that hard.
Would you want to force an hard core Atheist photographer to work at a Christian Fundamentalist wedding?
Yes. Public-accommodation laws serve an important public interest. Allowing refusals of service is a recipe for complete chaos. The photographer is there to provide a service on a for-pay basis. S/he is not a part of the proceedings any more than a waiter at the reception is.
The thing is, you are trying to shift the burden onto an innocent would-be customer when it is the business owner who must shoulder the burden that he or she created for themselves. The business owner advertised that his/her goods or services were available and people came in response to the advertisement. They shouldn't have to be humiliated and then forced to drive around looking for something else. You seem to be expecting that would-be customers must have a crystal ball or something.
The false-advertising issue is separate. Even if we allowed discrimination to override our public-accommodation laws, this issue would remain.