A few observations.
1. As a general principle, I believe that if someone opens a 'public accommodation' business this implies an obligation not to discriminate against certain groups in the provision of goods/services.
2. There are exceptions to the above, but I don't believe that they involve benign, immutable characteristics, such as race, ethnicity, sexual orientation, etc. (Benign meaning that they are characteristics that have no implications for any second party, immutable meaning that they are inherent traits that are determined by birth or beyond a person's control.)
3. To the extent there are exceptions, I believe that they would entail non-benign, non-immutable, behavioral based characteristics, such as outward expression of ideas/beliefs that are dangerous, harmful, truly offensive, or that an owner/proprietor finds morally objectionable. For example, if a bunch of skinhead me-Nazis flouting swastikas enter a restaurant, I believe the owner is in his/her right to refuse them service.
4. For goods/services that are of a highly specialized/customized nature, I believe that owners/proprietors have more leeway to refuse service. For example, an attorney should not be compelled to take the case of someone he/she finds morally repugnant, say a neo-Nazi. I have mixed feelings about the cake case, but in the end, I believe that the baking of a cake like that IS a form of artistic expression and thus the baker shouldn't be compelled to put messages on the cake he/she finds morally objectionable. We can debate about whether homosexuality is immoral. IF, however, the gay couple was requesting an off-the-shelf cake, and the baker had refused to serve them, then I'd feel much differently.
5. I come down on the side that the owner should just have served Huckabee. However, to me, this comes under #3 above such that the owner should not be compelled to serve her. Shilling for a lying, proto authoritarian who is a purveyor of hate is neither a benign or immutable characteristic. Were it me, I'd still serve her.
6. We will save ourselves a lot of anxiety and stress if we accept that humans by their nature are inconsistent and that few people truly live by a set of consistent principles, other than the principle to seek advantage over others, privilege one's own interests and beliefs, and apply 'principles' on a case-by-case basis as is convenient. Thus we have on one hand the Evangelical Christians arguing that they should, on moral (pseudo) religious grounds, get refuse service and human dignity to others they find objectionable but on the other hand possessors of an over weaning persecution complex who would howl and cry to no end were they every to find themselves on the other side of the 'morally objectionable' discrimination.
7. I find it fascinating how in DC politicos and pundits put more value in 'civility' than in 'decency.' So the Red Hen will draw the ire among Republicans for an act of incivility, but the same Republicans will overlook over and over and over again acts of indecency by this Administration, such as separating children from parents as either an political ploy, a cynical sop to a political base, and/or out of sheer malice. I do agree that civility is important, and I'd like to see more of it, but more than that, I'd like to see more decency and people on both sides of the aisle ready to promote more decency and condemn indecency when it occurs.