You should go into every game with an open mind and not pre judge any team/player. However, this is hard to do in reality. I was at a training session once where an ex PL referee said he would always caution a certain player the 1st time he did anything as this got him "off my back". Now is this wrong or is it managing your situation.
I have also showed up at games to hear the comment "oh no not him, he hates us". I can honestly say I have never purposely went into a game favouring one team or another even when I have had a problem previously.
My view on the Pickford incident is that the officials just got focused on the off side & missed the Pickford tackle. This is where the VAR guy should have stepped up but I reckon he was more focused on the off side lines. I honestly think Pickfords problems would not have come into the refs thinking at all.
strictly speaking in your first instance that’s conscious bias and thus subjective I.e. not viewing each incident on its own merits and deciding the sanction in advance. Similar to when Fernandinho always gets booked for his first offence. As for the Pickford incident you could well be right, however in my opinion Joe Hart got away with lots at City when he was the England keeper, English referees always seem to be that little bit lenient with well known English players.