I see where you're coming from, and I understand that you have a certain ideological value system of which I actually think requires quite a lot of courage to live by, especially when many people may disagree with you. That said, I do disagree with you.
The reason being, from a broad perspective, is that it is easy to classify things as black and white but it paints an incomplete picture. In this case, you argue for a persons right to refuse service from the viewpoint that people should have their own personal rights, no matter the consequences. The first problem I see with this idea is that it is dangerous to champion a society with an ethos of exclusion and derision with respect to widespread human traits that are non-controllable for the people that have these traits (being black, gay, a jazzfan etc.), especially if these traits are not hurtful to the people that have them nor to other people around them. Secondly, I also think that people should have basic human rights and should be able to make decisions about who they spend their time with in their personal lives, but in the case of the wedding photographer, she should have known that there would be many kinds of weddings that she would have to work, and as part of her job, that includes gay weddings. If she does not feel comfortable doing this, then she should not have accepted the position.
Finally, most people on this board are not diametrically opposed to one another, rather we tend to have opinions that are like vectors pointing in the same direction, but are of different magnitudes. I and many others on this board are with you on the whole freedom of choice thing, but are not nearly as extreme as you are for the reasons I stated previously, but that doesn't make us wrong.
She does not work for the government. Therefore she should be entitled to refuse to take pictures of whoever she wants for whatever reasons she wants. Now if she was a state employeed photographer then yes she shuts up and takes those wedding pictures.
That is the thing about believing in personal freedom (for me). You need to believe in it even when someone uses the freedom they have to do something you do not like. Personally I think the woman is an idiot for refusing to shoot the wedding but she is free to be an idiot. Just as I am free to take my business elsewhere because she is an idiot.
After her being forced to shoot that wedding (which is an absolute travisty of justice in my opinion) what is next? People being forced to hire her? If not then how do you justify her being forced to do something she does not want to do and a customer not being forced?
That right there is one of my main problems with republicans. They are all for personal freedoms as long as you are doing something they like with it. Like not getting married to someone of the same sex...