Fans are ultimately fans of the team and that tends to align them more with ownership than with players. If a player leaves your team via free agency for more money, there's a feeling of betrayal. If a player holds your team up for more money, that's resources your team can't spend elsewhere.
Fans tend to forget there's a third side they could be on, their own. Fans should press to be given an affordable, entertaining product. Whether it's a billionaire or a millionaire enriching themselves doesn't matter. The enrichment happens at the expense of the fan.