To be frank, I think the badge on the shirt underpins people's opinions way more than those ideological differences.I think the last page or two of this thread is a good example of why refs and law makers are somewhat on a hiding to nothing. The range of what people think football is or should be. The Idea that kicking an opponent should be allowed because it's a contact sport and it's a consequence of 22 men in a confined area trying to play with the same ball, while other look at the need to protect players as an important remit. You get Chris Wilder bemoaning the modern game when Holgate gets sent off, meanwhile Arteta is demanding more protection for Saka.
These ideological difference underpin people's opinion and shapes views on everything including the ref, the laws, VAR, commentators (eg whether someone is a "dinosaur" or a "proper football man").
I'm quite sure that every Brighton fan unsure about the Gilmour red, would be 100% sure it was worthy of a red, had that tackle been made ON Gilmour. Just as Wilder would have never questioned the Holgate red had that 'challenge' been made on one of his players.