The destruction may (may) be the fundamental application of the prohibition of Tasweer.So, our conclusion might be that we, as Americans, welcome, and respect, all Muslims, but we insist on our First Amendment demands that the religious freedom of one person stops at the "nose" of the other person. As for what we see as wonton destruction of historic sights in other nations, we will use diplomacy, but not force. If invited in by the lawful, recognized government of the nation, we will consider assisting but make no guarantees.
The description in the media seems consistent with the Islamic prohibitions on making, and the mandates for destroying, certain images, monuments and structures.
We saw it when the Taliban destroyed the Buddhist's statues; part of an assertion process.
Please see: Shakir, Abu Muhammad Abdur-Ra’uf. The Islamic Ruling Concerning Tasweer: Two and Three Dimensional Images, Drawings, Paintings, Photography and Sculptures. Zakee Muwwakkil Books, Philadelphia: (1998).
The destruction of historic treasures is a terrible thing, but not the only terrible thing in this world.
Regards — Cliff