Folks are treating the obvious bias on Fox News and MSNBC as something new, something to get worried about. I don't know about worried, but it for sure isn't new. It is old, although the medium - cable news - is relatively new.
My father was a lifelong conservative Democrat. As a kid growing up in Southern California, I remember that he avoided reading The Los Angeles Times published by the Chandlers because it was then a Republican paper. It is that no longer; it would now be characterized as a Democratic paper from the bias of its OpEd pages. Instead, our family subscribed to the Democratic Los Angeles Daily News published by Manchester Boddy, a paper which went out of business in 1954 and is not related to the current paper which bears that name.
During my father's lifetime - 1887 to 1971 - there actually were conservative Democrats. For the younger of our readers, those would be vaguely like the Blue Dog Democrats of today.