You must appreciate the difference in not wanting to work for a racist (refusing to work for the KKK to promote racist views) and a racist not wanting to do work for you (someone refusing to make invites for a mixed marriage for example).
Is there a legal--or perhaps more specifically,
constitutional--difference between the two?
If someone holds views with which you don't agree, such as a member of the KKK, then I agree that you should be able to refuse to do business with them. But if someone is gay or black or Asian, then that in itself is no grounds for refusal.
Anyone can refuse to provide a service to anyone, so long as the law does not require them to. In some cases, laws have been passed to require it in certain cases, such as various civil rights legislation. The difference between "gay or black or Asian" and "a member of the KKK" is that the former groups are (at least in Colorado) clearly protected, whereas the latter is not.
Though perhaps being a KKK member
is a protected class. I do notice that in the big list of protected classes in the Colorado law ("disability, race, creed, color, sex, sexual orientation, gender identity, gender expression, marital status, national origin, or ancestry") it lists "creed". I am not sure exactly how this is defined legally. The most "official" thing I can find is
Creed (Covered Under State Law Only) - Division of Human and Civil Rights - State of Delaware which appears to define it rather broadly, although its specific examples are all religion-based and this is Delaware rather than Colorado.
If it does count as a "creed", then one would not be able to turn away a KKK member as a customer for being a member of the KKK--though you could turn them away due to not wanting to create whatever product they ask you to. So a KKK member would be entitled to be able to come in and buy a standard product (say, a hamburger) but wouldn't be able to make people print something that's endorsing KKK beliefs.
And it's drawing a very long bow indeed to suggest that a gay couple is promoting gay marriage simply by getting married, something that is entirely legal. And I can't accept that people in a mixed marriage are promoting anything at all.
Two people of the same gender are inherently promoting gay marriage by getting married--if you are doing something publicly, you are inherently promoting it. That said, whether it is "promoting" it or not is not the important issue to begin with.