I have tried to do the same, signing up for the Flip Side newsletter, among other things. I think it’s still hard for me, an over-educated progressive, to understand the American right. Here are the problems:
1. Reality is often only reported in “liberal” news sources. A lot of information is censored on right wing sources.
2. Both types of news sources editorialize in the headline. Sometimes it’s hard to know they even refer to the same story.
3. People trying to achieve balance in reporting often relocate players onto the wrong team. For example, the Mueller report is not a “left wing” document and balance is not achieved by putting Mueller against a Trump surrogate.
4. “Liberal” sources already include plenty of right wing opinions. For example, David Brooks and Ross Douthat write for the New York Times. There’s no equivalent among the Wall St Journal columnists or Fox News hosts.
5. News stories found only in right wing sources are usually mendacious. For example, reporting about the Michigan ballot glitch without mentioning that it was human error and corrected before reporting the results.
Fundamentally, it’s not that we have differing information, it’s that we only accept information that confirms our world view. I can read dozens of articles written from the point of view that universal health care will destroy the country and not one will ever resonate with me. It’s just too silly to me.