A similarly large group will refuse to believe anything from a media source they believe is biased - and their standard for bias tends to be whether it agrees with their view of the world or not.
Let's get one thing out of the way: The media is going to be biased. Which issues they cover, how they cover them, or any number of other things can all create a false impression without a single lie being told. Sometimes that can even happen unintentionally if the reporter feels strongly about the issue and doesn't think carefully about how they might misinterpret or misrepresent.
But there's another point here: attacking an argument based on the source and not the content is still an ad hominem - a fallacious argument. There's no exception built into that for untrustworthy sources, because even they can be right sometimes.
Sometimes acting like there is such an exception is a useful shortcut. I don't worry about taking apart every Breitbart article that disagrees with my views; the belief that they are biased and likely wrong is sufficient to maintain my confidence in my opinions.
If I want to prove that point, though - whether to myself or someone else - then a higher standard of evidence than "I think they're biased" is required. That's where I have to figure out how they misrepresented the truth, explain how their evidence also fits a different conclusion, or talk about the parts of the issue that they didn't cover and why they're relevant. That can easily turn into a debate of its own, with one side talking about other aspects and interpretations and the other defending their original characterization. It's worth noting, also, that stating that a media company or specific reporter could be biased or has reason to want a specific conclusion is certainly relevant, as it applies to a motive... but is not by any means a complete argument, until information about how they misrepresented the truth is presented.
Also, the argument that a media source is biased in a specific way or to a specific degree is just as much of a specific point subject to debate as any individual article or issue's coverage is. One can certainly try to treat it as a fait accompli, and given the way most people view even those sources they agree with, it might be accepted without complaint. But even that doesn't make it automatically true.
In the end, frankly, there's no easy solution for the problems that bias in the media represents. Any solution other than a well-educated populace that's committed to the truth and to defending it properly seems like a patch. All of us, ultimately, need to hold ourselves to that standard.