No Bruce fans give a shit about his portrayal in the movie. It might hurt his rep for new moviegoers who never heard of him before but they probably don’t even care and I think in general he will be forgotten in a generation anyway except for like hardcore fans of cinema and/or martial arts.
Also, a key part of his story was his arrogance, it’s not a secret. He had to have a certain disinterest in what others thought of him because everyone in the Traditional Martial Arts community was telling him not to do what he was doing. He was always a guy who believed in finding your own path and creating your own style, and in those circumstances being arrogant was required to deal with the naysayers while still teaching to everyone else. Obviously, history has played out in favour of his methodology.