I loved the movie and discovered Mozart’s music through it. But, the movie doesn’t purport to be anything but broad fiction. Still a very, very fun movie.
Anything out of Hollywood, almost, is going to be a pack of lies.
Anyhow, even in cases where rivalries DID explode into unpleasantries, only scholars remember it today. Everybody else only cares about the music that stood the test of time. Who’s going to care about, say, rap music in 100 years?