Allsides.com sounds entertaining, I'll have to check it out.
I'm not sure there ever was such a thing as an unbiased media but the biases of the past seemed deferent and less overt. I get the sense that the biases that would have been obfuscated by news organizations in the past so as to appear "accurate" or "truthful" are now seen as virtues. I think they target their audiences with what they want to hear because that sells better than facts and they make it obvious so that the different audiences can easily find the narrative they like the best.
Your second statement is exactly what is going on right now. Rather than create an audience with a different approach they cater to what an already existing prejudice is and then make their stories around exactly that. It isn't journalism but rather it is pandering.
Allsides probably has their own biases as well but at least it is useful to see the stark contrast of stories about exactly the same topic and how two opposing networks or media outlets are able to come to completely opposite conclusions using the same information.
"Allsides probably has their own biases" Truth, but that really begs a philosophical question. Is it possible to create anything that is truly unbiased or is anything that we create going to be colored in some degree or another by our biases? I think the act of consuming news requires some level of critical thinking along with a willingness to hear message that we don't agree with so that have more material to sift through in our effort to find the cornels of truth. Of course, that process colors the information with our own personal biases.