It's a tiny percentage of people to be fair. On twitter I make an effort to follow fans of other clubs as I'm interested to know what they think. So many fans of clubs accuse the BBC in particular and MOTD of not favouring their club, something we've seen many blues say on this forum and especially on Twitter. On Twitter, City have many detractors, but that applies to every club. I regularly see "fans" slating Liverpool, United, Arsenal, Spurs and so on. It's hard but sometimes you have to realise and accept it happens a lot.
In terms of media bias, that goes on a lot in my opinion. In a world where clicks really matter, many media outlets will panda to the larger fanbases especially those with a worldwide fanbase. City's growth in the last decade has been extraordinary but we're still someway behind United, Liverpool and many of the other clubs who have existed at the top for a lot longer than City. We are getting there though, but the new territory has its pitfalls too. City will routinely be called out for its owners links to things like human rights and many small time journos will want to try to make a names for themselves and garner support through social media. I also think, like you, that City also get an awful lot of praise for the good things that go on at the club. Especially the football and the community work.