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.