The argument that the First Amendment only applies to government regulation is a misleading distraction.  Yes, it forbids the government from undertaking certain restrictions but it also expresses a fundamental American ideal and principle.

The Bill of Rights codifies God-given rights.  It is based upon America’s First Principals — that all Men are created equal, and are bestowed upon them by Nature’s God certain unalienable rights including the rights to Life, Liberty and the Pursuit of Happiness.  In case that was too vague (and thank God for their initial caution), the top 10 were enumerated.

If a business that claims to be part of the public square violates the rights put forth in the First Amendment (1A) then it should be shamed and condemned, regardless of it’s alleged rights as a private business.