Yes, I feel we do have to keep reminding Trump's base that he's part of the elite. Eventually they'll see it. It may take a long time before they do. Trump may have to break all his promises to his base before they see him for who he really is. But it's essential that we continue to remind his base until they wake up and see him for who and what he really is.
No, reminding Donald Trump's base that he's part of the elite discredit him in their eyes. All the members of his base care about is how much he hates Mexicans, Muslims, and everybody else they hate. It was enough for them to elect someone who lives atop a golden tower in New York City.
Donald Trump has a support base of mostly white, blue-collared workers. Many of these men live in the states known as the Rust Belt. They voted him into office believing he would revive the coal and steel industries. They don't seem to care if he is rich or poor. Reminding them that Trump that is part of the elite, one of the super rich, would not discredit him in their eyes. In fact, they admire him because he is a successful businessman. They are convinced he can and will use his business skills to bring their jobs back.
The Trump followers are supportive of his regardless of his elite status or wealth. He has successfully presented himself as a leader of the working class and they will continue to follow him. The Trump campaign had many blunders and insults without doing any damage to his election. So there is little to discredit him at this point.