In the EPL, agree not just one game, and it’s an FA decision not a club decision of course, but if there emerges a perception of positive/negative bias then yes they do try to avoid.You can't dictate who can and who can't referee your game just because they've made a bad decision against you.
I mentioned Mike Dean. Tranmere Rovers fan, so was directed away from Liverpool games mostly, only a handful of games in 20+ years of refereeing. And most of those were Merseyside derbies where he was considered a neutral. Apparently hated Arsenal.
Clattenburg was another who was seen to be a pro-Liverpool anti-Manchester referee.
Of course, there’s the clubs that referee support, which means they don’t referee those games, nor their rivals (eg Newcastle/Sunderland for Michael Oliver), or any other game for teams involved in a promotion/relegation battle with those teams.