Zappa was an extremely outspoken enemy of religion, government, commercialism, and just about anything else, so this song and album are right in character. Joe's Garage has parodies of a broad range of subjects - there's "L. Ron Hoover" and the "First Church of Appliantology," the Roman Catholic and Christian churches, lots of references to kinky sex (he also mocked that a lot), the "Central Scrutinizer" is kind of like Orwell's Big Brother - referencing government censorship, making fun of "dope and LSD" and snorting lines of detergent, the music industry in general... you get the picture.
The ban-on-music thing in the story stems from the government's "Total Criminalization" policy, where this new philosophy passes the legislature that states that "all humans are inherently criminals" and it's the government's job to keep making up laws to give them an excuse to throw everybody in jail.
Bottom line: You can't narrow the theme of the album down to one thing. If anything, it was more Zappa's general mockery of the whole capitalist-industrial military-religion complex, and mentioning Iran was just his way of saying "Look what could happen here! It happened there, after all." Seeing as how this came out before the PMRC targeted Zappa for obscenity in lyrics which led to parental advisory stickers on album, that kind of makes him a prophet.