As I pointed to earlier, there is a difference between discriminating against a person's circumstance of birth or protected characteristic, and discriminating against an idea.
Gay isn't an idea. Marriage isn't merely an idea.
Humans as a species value certain things very strongly
1. The right to have concentual sexual relations with a partner of choice.
2. The right to form a loving family with a partner of choice.
These are pretty fundamental stuff.
It's not like the right to buy a pepsi cola.
The argument of whether someone is born gay or whether gay is a choice is totally irrelevant.
Neither you, nor I, nor government, nor church gets to pick other people's partners for them, or gets to say "No" to other people's relationships.
Certainly, I can't just come up with a claim that interracial relationships are bad, or that people with blue eyes aren;t to marry people with green eyes. Or people that are into astrology aren't to marry people into astronomy.
For marriage the govt gets to intervene a little with rules that the people getting married must be above a certain age (because we don't deem children as being capable fully of giving consent) and must not be immediately related (presumably due to the danger of grooming). Churches can decide not to marry gays in their church, and this is OK, because Churches are not important to marriage. It's a private club with their private rituals which are tacked onto marriage.
I think it opens up a serious can of worms if we start operating on the precedent that "everything a person who happens to be in a protected class want to say/do/have made for them, is thereby an extension of that protected class"
If you sell wedding cakes or make wedding websites and sell to the general public then you shouldn't be able pick and choose the type of person you will sell to. Sure if someone is rude or threatening then you should be able to choose not to do business with them. But you shouldn't be able to deny them simply because YOU don't approve of who their partner is.
In the case of this website designer, they said they would (and have in the past) done work for gay people, they just won't do a gay wedding website.
Cool, But why not a wedding website?
They will produce wedding websites, but just not for gay couples. Sounds like discrimination to me.
But all of that aside, much like the cake shop story from a few years back, this doesn't come across as a sincere concern that there's lack of public accommodation due to a person's immutable circumstances of birth, this is one of those stories where the dialog surrounding it suggests that it's more about one sides desire to create an imposition and force someone to do something so that people can "prove a point" and pat themselves on the back.
People don't get married to prove a point. They do it to celebrate their love for each other and to exercise their natural right to form a family.
Why I get that vibe? Colorado is one of the most LGBT-friendly states there is, with ample amounts of business that will happily provide any service a gay couple may be asking for, so the conversation of "what if 100% of people in the city wouldn't do it/public accommodation" is largely a non-starter.
Irrelevant.
The argument of, "well just go else where" isn't a string argument.
Should we allow cafateria's to refuse black people just because there is another cafateria somewhere in the city that allows black people?
To use an analogy that highlights the tone of this public debate (but looking at it from the other direction):
If there were a conservative Christian area, and 29 of the 30 stores in town all put up signs that said Merry Christmas, and sold Christian-specific holiday decorations. But that 1 store out of 30 said "well, that doesn't really line up with my beliefs, so we're just going to say Happy Holidays, and and we're only going to sell non-religious or religion-neutral holiday decorations at our store"
Do you understand how irrelevant this analogy is?
The Happy Holidays shop doesn't have any Christmas trees in stock, they don't sell Christmas trees to anyone.
However the cake baker has ovens and flour and butter and make cakes and sell them.
The website builder has computers and a language and servers and skills.