And if you live in a town FULL of racists?
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.
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"
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.
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.
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.
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"
If, instead of simply going to one of the other stores, a small, but loud & vocal, group of Christian activists descended on that store and started demanding the store owner sell them a "Jesus is the reason for the season" decoration, and when the store owner says "sorry, I can't do that, I'll gladly sell you any other decoration I have out on the shelves, but I'm not going to provide that specific niche one you're looking for, but all of the other stores in town have them so you'll have to get it from one of them"
And they, in turn, replied back with "No, I don't want to get it from them, I specifically want YOU to provide this product and sell it to me", and when the store owner refused, they all claim "See, look!, he's discriminating against Christians, that's a protected class!, we're taking you to court!"
Would that come across to you as a good-faith complaint or any sort of sincere concern about Christians not being able to find public accommodations? Or would that come across more as the a mob ganging up on the one guy in town who's not sufficiently "bending the knee" and participating in the groupthink to the level of their liking?