Yes. The hat is real. They made a special extra-extra large MAGA hat to fit Lincoln’s head, which is 3 feet tall on the statue.
https://www.nps.gov/linc/learn/historyculture/lincoln-memorial-building-statistics.htm
In an unrelated issue, I have the actual footage of the Battle of Cannae. There are parts of it that are a little unclear and I will have to resort to CGI for some of the gorier moments, but for all intents and purposes it’s as real as the MAGA hat on ol’ Abe.