MLB can start to care anytime they want to start to care. Again, it's business, if this becomes a story that gets a lot of traction they will "care". For how many years did Major League baseball look the other way on domestic abuse or sexual abuse? When society forces them to "care", they "care".
Not that I want to single out MLB, that's the way it's always been pretty much everywhere. Nobody really cares until they are forced to.