Distributors Weinstein Co are "exploring legal action" because NBC rejected ads for their film about the Dixie Chicks' criticism of George Bush.
The Dixie Chicks admit audiences for their gigs have halved
The film shows the bad public reaction after the band's Natalie Maines said she was "ashamed" Bush came from Texas.
NBC said it was following its "policy of not broadcasting ads that deal with issues of public controversy".
The ad includes footage of the Iraq War and background on Maines' onstage comments in London.
Radio stations later refused to play the band's songs, while their albums were destroyed in the street.
The documentary Shut Up and Sing follows the country music group from the gig in 2003 in which Maines made her comment to the release of their latest album, after which they began to tour again.
The local channels of all the major US broadcasters have been showing the commercials.
Weinstein Co released a statement including reports from NBC's standards and practices department with notations saying the ads were unacceptable because "they are disparaging of President Bush", reported Reuters.
It also accused the CW network of rejecting the ad.
Harvey Weinstein, the studio's co-owner, said: "It's a sad commentary about the level of fear in our society that a movie about a group of courageous entertainers who were blacklisted for exercising their right of free speech is now itself being blacklisted by corporate America."
Weinstein has gained a reputation for aggressive marketing tactics, particularly during the run-up to the Academy Awards when he was co-chief executive of Miramax films.
But his spokesperson denied that his criticisms of the TV networks were just a way to get publicity.
Alan Wurtzel, head of standards and practices at NBC, told AP that even though the Weinstein Co had shown NBC its ad, it had not asked about buying air time.
If it had, they could have worked together to make the commercial acceptable to the network, as was the case with Michael Moore's Fahrenheit 9/11, added Mr Wurtzel.
The CW said a Weinstein representative had had informal discussions with a junior network official who questioned whether the network had the right programming to fit the ad, reported AP.
The CW added that it would accept the ad if commercial time was bought.
Shut Up and Sing is on limited release in the US from this weekend.