I've played through all three BioShock games, and all three are rather moderate political commentaries. The first two are about the flaw of making a utopia based on a single strict policy (extreme freedom and laissez-faire in the first and extreme collectivism in the second) without taking into account how human nature doesn't work with it.
BioShock Infinite is a game about the dangers of extremism. You can see aspects of the Founders and Vox Populi in the real world: the Founding Fathers are treated almost as legendary figures of pure good whose wishes should be considered for every decision (regardless of whether they would even have the knowledge and mindset necessary to understand the changes of the modern world), while anti-government sentiment is unusually common and can reach scary levels where people will outright state a desire to engage in violent revolt if a political decision doesn't go as planned. In the Infinite world, the Founding Fathers are literally worshiped as gods, with a religious mythology built around them that all citizens are expected to follow. Meanwhile, the downtrodden minorities forget the cause that they fight for and instead begin to irrationally hate the Founders, slaughtering children and civilians and essentially causing random chaos until Columbia burns. They're both too far deep into extremism to even consider the other side more than the most horrifying monsters on the face of the planet. Mix that with a lot of authentic turn-of-the-century prejudice, and you've got a melting pot of human terror.
The whole point of the game is that both sides have gone to the extremes of the right and left sides of the political spectrum. Elizabeth even romanticizes the Vox Populi as noble freedom fighters, only to realize that they've become just as monstrous as the Founders. They even repeatedly stated this during previews of the game, that both sides were extremists and you'd be forced to fight both.
Ironically, the outcry over everything kinda proves Ken Levine's point: everyone is so busy getting angry over the game "supporting the other side" that they forgot to look at how bad they're acting themselves.