"Turn the other cheek" doesn't apply to animals. They spit on you, you beat them up. They shoot at your church, you burn down their mosque.
St. John the Dervish and St. Ahmad rebuke you! (They're the only two Orthodox saints I can remember who were raised as Muslims and converted.)
Turn the other cheek applies to individual human relations, and is a call to imitate Christ. It does not apply to those 'who bear not the sword in vain', nor to the defense of other innocents. It is for this reason that there has never been a prohibition on Christians bearing arms (though in the earliest days, Christians couldn't join the Roman army until it was depaganized, since soldiers had to offer sacrifices to the pagan gods), though clergy are forbidden to shed blood (abused in the West by mace-weilding prelates, but
I digress). We Orthodox regard warfare as problematic, though--while we have specific blessings for arms, we also penance anyone who commits homocide, even accidentally or in a war under just legal authority.