I don't know any Liverpool fans personally and have never met one so couldn't say for sure.
There are large number of their fans who pull generally unpleasant stunts like bricking an opposition coach before an important game so that their opponents are on an adrenaline comedown during the match or setting off fireworks outside their oppositions hotel so they don't get a good night's sleep before a game.
You don't generally gets stunts like that from fans of other clubs around the world so they definitely have a higher percentage of fans who put a higher priority on a win than seeing their team engage their opponents in a fair sporting way.
This attitude comes from the top I suspect, Klopp could easily stop the diving, play acting and violent conduct if he chose to but doesn't. Their coaches and middle management have been proved to be thieves and cheats by hacking their opponents. All these people were hired by John W Henry who had shown not only here but with his US teams that cheating isn't an issue to him and he will do whatever it takes to cheat his way to the top.
Personally, I'd be livid if our club and players behaved like theirs, I don't think players like Robertson, Salah or Mane would be lauded and respected here the same way as they are by the Anfield faithful at the game or in the reporters box.
That's just going off the City fans that I know anyway. For us it's the competition and the challenge that's the important thing, sometimes we win and sometimes we lose but as long as we haven't been cheated then it's all the same, that's what sport is about.
Having said all that I think there's probably Liverpool fans who feel the same way. They'll be embarrassed by the antics of their players and of their fans who disrespect the game as a sporting event so badly. It's just that the internet amplifies the voices of the crazy people on the outskirts of all conversations so the more rabid Liverpool fans are the ones you hear of as they're so out there and laughable.
Then again, it may well just 'mean more'.