We now have data showing that the left tends to read both mainstream and left sources. While the right tends to live in their own little Fox-Breitbart bubble. This means that the right gets news from extremely biased sources with no anchor in reality. While the left tends to read and share a wider variety of media. http://www.cjr.org/analysis/breitbart-media-trump-harvard-st...
It's also been shown that the right is more likely than the left to distrust the fact-bearing mainstream media [1], because a strategy of the right, as in some authoritarian countries, is to generate distrust in media that they do not control.
https://www.nytimes.com/2017/02/04/opinion/sunday/why-nobody...
So no, both sides do NOT do it equally. The right does way more to taint real sources like the NYT as biased.
[1] within mainstream I'd tend to separate profit-seeking and independent/family-owned media. But you can lump them together for purposes of contrast with GOP-donor-funded conservative media.