This is a lot more common, but I wouldn't call this proper skepticism. It's usually just people being cynical and biased in their own way. They've subscribed to a political tribe and social media echo chamber that happens to be opposed to something in Nature, and that's the reason why they're doubting whatever is written in Nature, with some made-up justification that sounds plausible only within that echo chamber but is transparently wrong to people not caught up in that particular group think. That said, actual skepticism should be applied everywhere, including towards Nature.
Do you think cynical mistrust (so-called "scepticism") truly is more common than lack of healthy scepticism towards information provided by trusted sources? Or is it rather more obnoxiously salient? Someone who rejects Nature claiming that the Earth is an oblate spheroid is much more likely to make their voice heard than someone who would happily accept whatever is published in a scientific journal with no question whatsoever.
Either way, at face value, I do agree that cynical mistrust (especially when partisan) is more immediately damaging to society than uncritical absolute trust, regardless of each of their relative frequencies. However, I do believe that each of these phenomena reinforce each other in a vicious cycle. The contrarian denialist feels vindicated when he sees the blind acceptance placed on certain sources by the naïve truster on the other end of the political spectrum. The naïve truster, on the other hand, feels that any criticism or questioning directed towards trusted sources on his side is to behave like the contrarian denialist would. Hence the mutual polarisation.
