I think this is the order of operations:
Conservatives believe bizarro conspiracy theories because they need to assign the ills of society to anyone other than the responsible ruling class.
Liberals point to this and say “See, look at this foolishness, if you don’t want to end up a rube like this, you need to trust The NY Times and WaPo and CNN, etc.”
Thus, leftists that are otherwise critical of capitalism but still want to be seen as being part of reasonable society, develop a bias of taking those sources at face value least they get branded with the scarlet F of fake news.