I got to thinking about this the other day after I saw a post on Twitter where a fan of another team, I think the Padres, was gleefully reveling in the fact that we had lost a pitcher to free agency with another team, AKA Anderson. Now, the Dodger-Giant antagonism goes back to the days the team was in Brooklyn. The two boroughs basically did not like each other. But for years, the Giants had the better team. But in the dog days, tempers would get short, and occasionally, fisticuffs would break out.
Today I think fans who dislike LA do so because the team has been so successful the last 10 years.