I agree with your thoughts, but you are not quite right regarding the law, it is a bit more nuanced.

The law allows people to not bake a "gay" wedding cake for a gay couple if other bakeries exist and are willing to do so. It does not allow a bakery not to sell products to gay couples.

So, the restaurant had no legal right to discriminate against the Christian group simply wanting to eat at the restaurant. Had they asked the owners, to serve a cake that said "End Gay Marriage" in bold letters on it, the owners could have refused provided there were alternatives.

Regarding the Christian baker, if your bakery is the only game in town, it becomes more problematic if you refuse to bake the gay couple's cake. Like the baker, the gay couple has rights including the right to pursue happiness (and a wedding cake is part of that pursuit).

That is why in each case where someone asserts "their" rights not to serve someone the courts look at the activity and the underlying religious belief and looks for the "best accommodation".

Using the baker as a case, being the only baker in town, the court might rule the baker must bake the cake, but perhaps not put the ornament on top... the gay couple gets their cake, the baker just baked a cake.

The problem is when progressive liberals or religious conservatives try to force behavior on people instead of looking for reasonable compromises. Trying to force people to violate their beliefs is not the answer.

Meanwhile, as a Christian, I believe Jesus said, "do unto others as you would have them do unto you". I am unconvinced denying a gay couple a wedding cake or a Christian group a dinner fit with that.