Conservatives may think that some "liberal elite" is dominating the discourse on social justice, but that is because activists on the left are the only ones addressing inequity.
Academics who have spent their entire professional careers studying topics like race, economics, history, and policy have come to a conclusion that may seem liberal to those on the right, but that is because conservatives would rather uphold the status quo.
The same goes for Hollywood; celebrities are just using their reach and public presence to speak about social justice. It would be irresponsible for them to stay silent on issues of inequity when they have the privilege to speak up and be heard. Through their mediums, they can share stories that help improve society.
As for the news media, they are tasked with reporting facts. Just because the facts do not always fit into a conservative narrative does not mean that they are representatives of some elite class.