Let’s face it, they do not destroy the cross because it offends them, they destroy it because it convicts them.
Bingo. We have a winner.
To them, the cross is like a mirror, and their reflection horrifies them. They'd rather not look at it.
Today, the atheists fear of Christian icons is nothing short of irrational. They seem to either tremble in fear, or lash out with rage. (Deep inside, they know they have but little time. Demons always screech the loudest when they're being cast out.)