Both men are New Yorkers about the same age. Both Pres. Trump and “Punchy” come from the Entertainment World.
My guess is something happened between the two men a long time ago. Trump has gotten over it, Punchy has not and will not. Maybe they both wanted the same woman and The Donald got her first. Knowing how much Mr. Trump loves to gossip, maybe this woman told him something about DeNiro that was very personal and very embarrassing for Bobby. I can imagine Trump letting that info slip at just the wrong time with DeNiro knowing about it.
These Hollyweird types are so out of touch. They are doing exactly what Trump wants, playing right into his hand. The kind of display during the Tony’s is just what po’s and energizes Trump’s base, most of whom, by the way, can’t afford the ridiculous prices of Broadway shows.