Big corporations are, in many ways, functionally equivalent to governments -- like a government, they are soulless collectives with massive power. One of the airports in New York--either JFK or LaGuardia, I forget which--is privately run, and a friend ended up in jail for something he would have been constitutionally protected doing in the other airport.
This is where I part ways with my libertarian friends who look only at private vs public rather than individual vs collective. You're right, there's no free speech protections against a corporation shutting you up, but...there should be.
(And I can't believe I've somehow placed myself on the same side as a church, especially a book-burning hate-mongering church. Sigh...)