It appears real bu apparently done as some sort of a joke and has no real political consequence.
Good click bait though.
Andrew Bates
@AndrewJBates46
At the Shanksville Fire Station, @POTUS
spoke about the country’s bipartisan unity after 9/11 and said we needed to get back to that.
As a gesture, he gave a hat to a Trump supporter who then said that in the same spirit, POTUS should put on his Trump cap. He briefly wore it.