This is an interesting one. I suspect I'm far more liberal that most of the folks here (Joe Biden is too centrist for me, for example), but I think there is some nuance and I really don't know where I'd draw the line.
I'd also note that what I'd like the law to be bears no resemblance to what the law is and I don't know enough about constitutional law to talk about that part, either.
However, let's assume you want to hire a wedding photographer for your same-sex wedding. I think the photographer would be well within his/her rights to say "Sorry, not comfortable with same-sex weddings", but I'm less happy with a cake decorating place with a store front refusing to decorate a cake. Less happy, but not unhappy. If a store refuses to sell a gay couple a pre-made cake, then I have zero sympathy.
For me (again, not the law, just my opinion) the fact that a service involves creative work is relevant (selling me groceries is not a creative act. Making a cake and decorating it is). The fact that the person providing the service goes to you instead of you just coming to them seems to make a difference (IOW, they show up at your wedding vs. you go to their store and buy something for your wedding). There's also a matter of competition. The more competition, the less I'm concerned about individual acts of discrimination.
I think I'm fine with a web designer refusing to do work for a gay couple. They are generally individual contractors and can refuse work on the grounds that they don't feel like it. Plus, there are eight bajillion web designers out there. It's no real hardship.
How closely does this line up with the actual law? Beats me.