Is Fox News part of the mainstream media? If not why not? If so why so? Can you define what constitutes the mainstream media? What is the boundary that separates mainstream media from the media, says who, and by what authority?
Yes. However, behind the scenes they are run by only a specific faction of the Republican Party, and so a lot of views which they seem to espouse are only bait to keep the viewership of a different type of conservative audience. It's basically like if the Wall Street journal was trying to appeal to Trump supporters, and doing a good job of it. Is it propaganda? Yes. Just coming in from a different angle than the other mainstream networks. Those news anchors who espouse "controversial" social beliefs are just kept there for the ratings, but in reality are kept on a short leash. Witness Lou Dobbs. He got too pushy about immigration and they showed him the door. And he was considered a very moderate Republican. (I mean it wasn't because his views were too extremist) They don't have the same agenda as CNN, but let's just say they don't have the same primary agenda as the majority of their viewership either.
