Does a venue or the organizers of an event at a venue have the right to surpass the freedom of people who attend an event?
Yes. For a very large number of reasons.
The Constituion only guarantees that government will not infringe on your freedom of speech, etc; it does not limit the right of a private person/organization to expel you from their premises or fire you from a job for exercising your constitutional rights. A lot of people think they can exercise their constitutional rights without repercussions; they are wrong as far as private persons/organizations go.
In a word
YES!