NYT produces plenty of "fake news" and biased hypocritical trash. All of the big media outlets are flaming dumpster fires, regardless of where they are on the political spectrum.
There's been a few occasions where I've found an interesting article on Fox News and I won't share or link it here or on Reddit, because I know that the bias is so strong against Fox as an organization that few people would consume the content with an open mind. So I go and track down another outlet covering the same story and link that instead. I'm sure other members here do the same sort of self-censorship, essentially. That's part of why you'll see 6000 submissions from NYT and only 90 from Fox.
> So I go and track down another outlet covering the same story and link that instead.
That's exactly what I do on Reddit. I haven't had occasion to share a Fox News link here, but I think I would do it because I trust this place more to make judgements based on the content of the article.