The Kennedy Center is legally required to sustain itself through private funding and ticket sales. It also offers plenty of free performances.
https://www.kennedy-center.org/globalassets/news-room/annual...
None of the federal money pays for expenses related to the actual programming and operations of the Kennedy Center, it pays for the building and grounds, which has a separate purpose as the federal memorial to JFK and is also used for a variety of public events and educational functions outside of the Center's performance arts programming. The parent comment asked why the government pays for opera (it doesn't, maybe through a modest NEA grant or something), not "Why does the federal government pay for federal monuments and public spaces?"
Is this a joke? Literally the first expense listed under federal appropriation is "Operations". In theory they don't pay the producers of shows with the same money that comes from the government. But given that operations and maintenance are necessary to hold performances, and money is fungible, the distinction is meaningless.