Re: I was initially attracted to the majority opinion in 303 Creative
I understand those arguments. To be honest, I'm not entirely sure about what I came up with. It's a synthesis of the position I inferred from the dissent. Particularly, on page 34 of the dissent (which is illuminated by some earlier passages):
"...the Accommodation Clause and the State’s application of it here allows Smith to include in her company’s goods and services whatever “dissenting views about marriage” she wants; and contrary to this Court’s clear holdings that the purpose of a public accommodations law, as applied to the commercial act of discrimination in the sale of publicly available goods and services, is to ensure equal access to and equal dignity in the public marketplace..." [The Court's holding was that it's purpose was to remove the offending ideas from the public dialog.]
I see that argument as being like a card shop that sells wedding cards which only refer to traditional weddings (or do not obviously advertise same sex weddings). If a customer asked to see same sex wedding cards and the shop keeper says we don't sell those, the customer is not getting any less than anyone else. If the shop keeper refused to sell ambiguous wedding cards in stock to a particular customer because they knew or suspected those would be used for a same sex wedding, this would clearly be against the law. As a public accommodation, the business must treat customers with equal dignity and respect regarding protected characteristics. A way around this would have been to take such bookings only privately, perhaps by referral. You could even have a sign reading "ask me about these other services I offer privately". Private contracting is not covered by public accommodations law.
A public statement saying "We don't make websites for same sex weddings" is not unlike a statement saying "We don't make websites for interracial weddings." If this doesn't offend you as a human being in the modern age, then I'm not going to win this argument. To me it serves to delegitimize and stigmatize a person's choice in life partner. That goes to the core of a person's dignity. That's exactly the sort of mischief that these public accommodation laws are intended to capture. And if you think such a statement would be a stretch or might not be protected by this judgement, all I can offer is that there are still people who insist that the Bible forbids racial mixing.
Now, to your question:
"To be allowed to politely decline to create same-sex wedding websites, the designer would either have to state on every site she makes that she believes that marriage is between a man and a woman, or be forced out of business? It's not enough for one's work to be neutral, every case has to expressly state their beliefs?"
To be very clear, it would only be the wedding sites that this would apply to. As I see it, it's not enough to be neutral if you're not willing to be neutral for everyone. There previously would have been (and I think I agree with this) no right to refuse to make a website for one customer that is offered to others (I know they are all unique, but that's beside the point...), so if a same sex couple for whatever reason were willing to have a website that communicated the designer's belief that their wedding was not legitimate, she could not refuse to do it for them. Not as a public accommodation. It would be akin to the refusal to sell merchandise I mention above. Privately, you can refuse any commission. You don't even have to give a reason.
I recommend a careful reading of the two opinions. First the majority, and then the dissent, and then reread anything that you might want to take another look at. Both of the opinions are well written, and I can't come close to paraphrasing or reconstructing their arguments.