It's hard to know if they genuinely can't spot it, or if it's wilful ignorance used as an attempt to get more people to agree with them. I suspect it's a mix of the two, as they're not all thick and some no doubt realise the 'woe is me' card can get some people on their side.
The Daily Mail and Sun tabloids are some of the most widely read newspapers here in the UK, both are right leaning (especially the DM). So there's no silence there. But they'll still piss and moan about being silenced or mocked, while simultaneously pouring scorn on The Guardian and its ilk - despite them having a much lower readership.
You can tell The DM and Sun journalists probably don't even believe half the stuff they write, but they know their audience and ensure they cater to them.