You're quite right of course, DMcG, the word 'desecrate' does indeed denote rendering non-sacred a holy object or place, and it was ill-chosen. Although common usage does include 'to spoil or damage a treasured thing'
But venting one's anger on a statue annoys me because the sculptor has spent endless hours creating it, it stands in a public place and the damage/ graffiti offends the public, and the protest could be made in other, more civilised ways.