The key here is to distinguish between three things: a) established facts b) controversial facts and c) opinions. Now, the whole classification is somewhat subjective, thus it is tricky, but if you want to appreciate - and I mean appreciate, and not prove to yourself once again you are right and they are wrong - different points of view, you need to make those distinctions.

For this specific climate change thing: if the news story gets established facts wrong - e.g. claims that Earth is literally flat, or that Earth is literally 7000 years old, or that study X was about Y and had these numbers, when the story actually was about "not Y" and had completely different numbers, etc. - that is a disqualifier, there is no use in reading such story and such news source.

If they get controversial facts wrong - i.e. claim that critically acclaimed climate model is actually flawed because of reasons X, Y, Z or that a study about climate that makes conclusion A instead should be making conclusion B - you may very well disagree with them, but that disagreement is not a disqualifier - at least it should not be if you are genuinely interested in discussion and not confirmation of pre-existing beliefs. It doesn't mean that article is right - the criticism may turn out to be completely wrong - but the mere fact of disagreement should not be a problem.

If they get opinions wrong - i.e. they advocate political solution A to a problem X while you favor solution B, then again they may be wrong, but this is the normal course of politics - many solutions have tons of trade-offs, and even if it were possible to always identify the superior one (which is not), it'd only mean millions of people that support sub-optimal ones are wrong, and given that there's no guarantee you'd not end up - and frequently - among those, there's no reason to refuse to even consider alternative perspective. Again, you do not have to agree with it - but having different opinion is not a disqualifying thing for a news source.

> I'll happily read a conservative news story that understands facts but many ignore/lie about them to drive their political agenda.

The same can be said about the other side. All too often our ideology drives what we believe rather than being able to see and sift through people's arguments.

The problem is that "both sides" tend to read to reinforce what they know rather than to challenge it. Why not try to understand someone's argument.

For example I've talked to several people who 1) agree climate change is happening but 2) disagree with most of the people who are very pro cap-and-trade or emissions limiting.

I have plenty of conservative people(one of the benefits in living in a rural area) who I love having a solid discussion with. I was specifically talking about conservative news sources.

Fiscal conservatives I totally grok(and don't disagree with some select things). However the current mainstream conservative bent seems far from that. If you have no basis in facts how can you even work towards any common ground?