Is it any worse than sealing up this gate, building a cemetary in front of it, and then building a huge mosque right on top of another religion's holiest site?
It will be a propaganda for Al Qaida to paint Christians as barbarian more than their own extremism and let them paint Christians as uncivilized in their perspective. Extremism often lose international public support, and when you lose public support, you are in bad shape in the war against terrorism. Al Qaida is likely viewing the move of Dove as an opportunity to fuel more attacks through angry local Afghans and view Dove supporting Al Qaida for their purpose of terrorism. In other words, Dove is supporting Al Qaida and terrorism in the perspective of Al Qaida.
I believe that the Romans did that.