First of all, it is worth noting that the linked article is from December 2013. Since then, a number of things have happened:
(1) in May 2014, the Colorado Civil Rights Commission affirmed that the baker violated the Colorado Anti-Discrimination Act;
(2) in August 2015, the Colorado Court of Appeals rejected the baker’s argument that his religious beliefs were sufficient in this case to justify a refusal of service;
(3) in April 2016, the Colorado Supreme Court declined to consider the case;
(4) in June 2017, the US Supreme Court agreed to hear the case; and
(5) in December 2017, the US Supreme Court heard oral arguments regarding the case.
So it is worth noting that this case is not yet completely over, and that its resolution likely rests in the hands of Associate Justice Anthony Kennedy (unless the court decides to rule on a narrower issue, in which case we might see something like a 6-3 or even 7-2 decision). On to the actual question, then.
If you are just asking whether or not Judge Robert N. Spencer made the legally correct decision, then the answer is clearly yes. There have been laws protecting certain classes of people at both the state and federal level for quite some time, and the owners of this bakery unambiguously ran afoul of them. Spencer really had no choice but to rule against the baker. Honestly, people should be happy with how the process has gone no matter where they stand on the underlying issue. At each step of the way, those involved have stayed well within their Constitutionally mandated roles, rendering decisions only on what they are empowered to adjudicate and then sending it along if and when questions remained. That’s how the system is supposed to work.
But if you’re asking a larger question about what an ideal society would look like, then I think it gets more complicated. In an ideal society, we wouldn’t have laws that carve out certain protected classes. But in an ideal society, we also wouldn’t have an unresolved history of oppression that makes such laws necessary. The existence of protected classes is a sign that we are still in the process of forming a more perfect union. Yet they are also a sign of our commitment to that goal. So the fact that they would not exist in an ideal society does not entail that they ought not exist in our as yet imperfect society. Nor does it entail that eliminating them would automatically get us closer to being an ideal society. After all, a society is more than its laws. And the difference between the times before and after the existence of protected classes will be found not in our laws, but in the hearts and minds of our people. But even if it’s hearts and minds that must ultimately change if we are to end oppression, laws are ways of reducing some of its most serious harms in the meantime.
To answer your specific questions, though:
(1) No, the owners clearly did not have the right to refuse service in this case under the relevant laws.
(2) I’m not sure where the talk of bankruptcy or shutting down is coming from. Masterpiece Cakeshop is still open and receives enormous financial support from supporters all across the country. But if the shop closes down after the case is decided by the US Supreme Court, it will be for no other reason than because the owner took a gamble and lost—no different than the risks taken by every other business owner every single day.
(3) All businesses already operate under the same rules about whom they can and cannot refuse service to and under what conditions. Regardless, it’s unlikely to affect me—straight, white, male—in any way.
(4) Laws cannot change minds, so laws prohibiting discrimination cannot force anyone to agree with or approve of anything.
(5) I dine close to people wearing neither shirts nor shoes every time I visit my mother in Florida. She prefers the outdoor restaurants down there, and none of them enforce such rules.