Climate protests are symbolic demonstrations that are not intended to destroy the art, but rather ramp up public pressure on governments to halt destructive new fossil fuel licensing and production.
They don't choose random artwork, they're actually careful into choosing which artwork to use to protest from. Plus climate activists protesting at art museums isn't a new thing.
https://www.npr.org/2022/10/26/1131377513/museum-protests-famous-artworks-history