Middle Eastern Christians are Eastern Christians. Even if I were to accept your basic contention that these 'similar interventions' are in any way equivalent - which I don't - they offer a sharp contrast to Western Christianity's history of frequently disastrous and usually counter-productive actions in the Eastern Mediterranean from the First Crusade all the way through to the Sykes-Picot Agreement and the Bush invasion of Iraq.
Western Christianity's attitude towards Eastern Mediterranean Christianity over the centuries has often seemed to combine elements of Arnaud Amalric's approach at the 13th-century assault on Beziers, and the American military's attitude at the Battle of Bến Tre. Caedite eos; novit enim Dominus qui sunt eius. It became necessary to destroy the town to save it.
But perhaps a topic for another thread; I'm not sure we want to combine an already reported genocide derail with a tangential handbags at dawn denominational bitchslap.