I think what sets Liverpool aside as a club, and one of the reasons it gets so much grief from opposition fans, is that it has always felt anti-establishment. For example, going around and referring to managers as 'Mr. Ferguson' (a very odd affectation by united fans) would never really catch on with Liverpool fans. For example Kenny Dalglish has a knigthood (not a fan of that myself, but oh well) but you would never hear him referred to as 'Sir Kenny Dalglish' (or very rarely at least). Liverpool fans have never really got on board the whole 'England, FA, LMA, greatest honour managing your country' etc. and I think that, more than anything, gets under the skin of a lot of fans in the UK, surprisingly from smaller clubs (where supporting England is all they have, really). It's Liverpool's independent ways that irritates them.
I think there is a lot in what you say.
Liverpool the city, Liverpool the club, and the people of Liverpool generally do not suffer fools gladly, and they bow to nobody. It takes guts to be a maverick and to willingly be an outsider. In a nutshell, Liverpool FC and its fanbase do what others wish they had the balls to do, but don't. We don't need to be media darlings, and we don't actually want to be anyway. I couldn't care less about the England football set-up, the English media or the prevailing xenophobia so revered within vast swathes of English culture. I love England the country, it's generally beautiful, but I have little time for English culture. I grew up wanting to play for Liverpool, but had no interest whatsoever in aspiring to play for England.
In many ways, we are what so many others wish they could be. They don't have the balls or the mentality to do it their way. Instead, they basically just do as they are told. Seeing LFC and Liverpudlians ripping that up and doing it their own way just throws their own timidity into sharp relief.
I see myself as Liverpudlian and European, but not particularly English. Liverpool is a port, so is cosmopolitan. In general, Liverpudlians travel and see the bigger picture. Scousers have travelled everywhere for work and/or to follow LFC over the decades. Go anywhere in the world and you'll find someone from Liverpool. As a City, as a club and as a fanbase we do not buy into the little Englander mindset. There will always be small minds that hate us because of that.