Well, rather than engage in amateur psychoanalysis :-), I think there’s a point to be made, here.
Those of us with a libertarian bent have difficulty with the baker/gay wedding situation. That does not mean we have a problem with LGBTQ rights or legalized same-sex marriage; it simply means that absent a prevailing government interest, it seems untoward to us to see the government ordering a private individual to do commerce in a way that violates their deeply-held religious views.
Legally, there are several questions afoot. Can the government effectively argue that there is a “prevailing interest” in ordering the baker to do business, when the alternative is that the individuals can simply walk next door to another vendor that will be happy to provide their cake? This fact alone makes the baker situation much different than southern segregation, where there was actual harm involved.
Then, as a private individual, does the baker not have the right to exercise their rights of religious free exercise at all? Could the baker make a list of denominations they will support weddings in, omitting those that practice same-sex marriage? Could they say they only bake wedding cakes for Catholics and Baptists? What if they smiled, took the order, and immediately subcontracted out the work to another baker who has no religious issue with same-sex marriage?
At what point are they allowed to exercise their beliefs?
Personally, I think the matter is a bit moot; as a practicing Muslim, I would have no problem baking somebody a cake for a same-sex wedding; but obviously, some people do. And these people have rights.
I don’t know where this ends up, but I have this gnawing feeling that we’ve leaned a bit too far on the accommodation side and need to remember what the 1st says about free exercise.