Here's the situation:
A man came in to a bakery looking to get a bible shaped cake. After the cake was agreed upon, he eventually wrote down some words and asked the baker to include them on the cake in addition to two men toppers with a red X over them. Because of the vulgarity of the words and her disagreement with them, the baker refused. Because of the refusal, the man filed a civil rights dispute, as he felt he wasn't being allowed to express his religion and was being discriminated against because of that.
The baker, on the other hand, says that no one should be required to provide a message with obscenities in it, regardless of if it is has to do with anti-gay work or not. It is, in her belief, within her rights of free speech to refuse to write a specific message.
It's interesting to compare, because there was recently another case in Colorado that some will probably try to compare (basically, a bakery refused to make a cake for a gay couple, and the court told them the bakery it was illegal to do so, and that a bakery can refuse to write a certain message, but cannot refuse to service a certain client because of their romantic affiliations).
But are they the same thing? Not really. Even though this woman was clearly uncomfortable with the anti-gay message, she wasn't the one telling him not to be that way. While she thinks that everyone should love each other, she did offer to make the cake still, and give him the icing bag that he would need in order to write the words himself. Which, I think, is more than he deserved.
This man is trying to argue his right to practice his religion is being impeded because she refused, but I can't see how that's possible. She basically handed him the bag and allowed him to write it. Isn't it impeding her personal moral or religious beliefs to try to make her write it? I think so.