a conservative station (which Fox is) play the Simpsons and Family Guy.
I could be wrong, but I think it's important to maintain the distinction between the Fox Network and Fox News. While it's true that both are owned and thereby controlled by the same person, AFAIK they operate under entirely different conditions (different heads of programming and etc.)
Both are driven by one thing: advertising dollars. Both try to bring in more advertising dollars by appealing to a niche demographic. Fox News clearly panders to the conservatives of the country (to see this, one only needs to see the anchors speak about Reagan...they practically have hearts appearing around their heads, they're so in love with him). Fox News hit on the fact that conservatives had heard the myth that the liberal media was perpetrating lies and bias so many times that they felt they were being underserved. Bada-bing, there's an audience waiting to be snatched up.
Meanwhile Fox TV generally aims for a significantly larger demographic that is (more-or-less) politically agnostic, skews younger, and is interested in more edgy entertainment than the folks who would watch CBS. As an entertainment company, Fox TV is politically anarchic, bending to the will of whatever it is people will watch. The politics of say,
24 are quite different than those of
The Simpsons.