Public accommodation laws are not about beliefs they are about equal treatment of the public in businesses open to the public.
And they can believe whatever the fuck they want what they can't do is violate the law with no consequences. The whole baking a cake for certain people is a sin thing is the purest most unadulterated bullshit I have ever seen outside of a political campaign
Hey I can believe that I should only do business with blondes with blue eyes and big tits but that doesn't mean I am justified in declining service to everyone else
In that they are forcing through government power private individuals to do things they do not want to do because other private individuals want them to do it, they very much touch on any number of rights held by private individuals. I have a right to choose not to associate with other people; they do NOT have a right to force others to associate with them. Because of this, public accommodation laws, in and of themselves, violate the Constitution. It is one thing to say that
public sector entities, such as government agencies, must service everyone. It is entirely another to say that private sector entities must do so.
Furthermore, to say, "They can believe what they want; they just can't practice it" is to say "They cannot believe it". A major problem with left-think on this subject is that it conflates "belief" with "thought", and assumes that one's beliefs are merely thoughts in one's head, divorced from one's actions. The exact opposite is the truth: one's beliefs are NOT what one thinks, or even what one says. What a person DOES is the truest measure of what he believes, particularly when circumstances are most difficult. The First Amendment recognizes this by guaranteeing not only "freedom of religion" but also "the free exercise thereof".
You are still arrogating to yourself the right to approve the beliefs of others. You are saying, "They have the right to believe what they want, so long as it is acceptable to most people." The First Amendment doesn't exist to protect belief that is generally acceptable to society at large; if it's acceptable to most people, it doesn't NEED protection, because it won't be attacked. The First Amendment exists precisely to protect belief that most people find repugnant.
And yeah, I actually think you should be free to restrict your business only to well-endowed blondes, if that's what you want to do. Of course, I also think you should be free to avail yourself of bankruptcy court when your business closes two months later. What I DON'T think is that you should be legally required to pretend that you like skinny brunettes if you don't choose to.