Would they deliberately turn away profitable business? Why yes, they would, if they have received threats or bribes.
Some businesses are not in business to make money. Their purpose is to spread the party line. If they lose money, rich leftists make up the difference.
Any threat/bribes to suppress a film in this way would be all over the internet.
This is a distributed control system. Too many conservative/normal people (theatre managers) involved for this kind of manipulation to be contained.