If the Court rules in favor of 303 Creative, then one day American Christians may legally refuse service to non-Christians, Christians who belong to other denominations, Christians who live differently, and atheists.
Only if they are not providing a public accommodation, in which case, there will be other available service providers, and no one will care.
The crux of the state's interest in telling merchants whom they must serve is competitive pressure. If discriminating against a group confers a competitive advantage - e.g., a luncheonette attracting white customers by excluding black customers - then competitive pressure may result in that group being denied access to the market for those services, and the law can prohibit that discrimination. But if discriminating does not in fact deprive the group of access to a competitive market for a relevant service, the law has no business telling anyone how to run their business.
The question here is not really about what constitutes "speech" or the free exercise of religion. Without parsing which of those privileges or combination of them is at play here, the circuit court in the case accepted 303's argument that the Colorado statute conflicted with the artist's first amendment rights and was, therefore, subject to "strict scrutiny" by the courts. The circuit then considered whether the state's interest in assuring all citizens access to commercial services trumped those first amendment rights. Thus, the case is about reconciling competing interests, not whether some conduct or other falls on one side or another of a the first amendment line.
The circuit court looked at whether 303's refusal to serve gay couples deprived those couples of access to the web design market, or, as the court put it, left them with access to an "impaired" web-design market. That's a good test, I think, but the court badly misapplied it by finding that a market lacking a unique participant (in this case 303) is ipso facto sufficiently "impaired" to support the state's compelling interest. I suspect SCOTUS may apply the same legal reasoning but find that 303's discrimination does not impair the web-design market sufficiently to implicate the state's power to protect access to that market.
So, yes, if SCOTUS holds for 303, you will be able to discriminate against anyone for any reason, so long as those you won't deal with are not seriously inconvenienced by you and people acting like you. That is a question of fact, and I doubt Ms. Smith will have any trouble proving that many of her competitors are perfectly willing to provide web design services for gay couples in her area.