Quite. Frankly, I'm sick and tired of European pseudo-historians framing every little clash between some monolith called "the West" and some vaguely-defined but apparently huge, scary, evil, "Other" monolith called "the Muslim Empire" or "the East" as a crucial struggle that saved the good, noble, progressive Western European civilization from conversion, slavery, and death.
If the Persians had defeated the Greek states and conquered them, they would've probably been western outposts of the empire for a while, their culture preserved like in any other provinces, and I think Greek influence on whatever the "West" is is massively overblown. Had the Ottomans taken Vienna, they'd still have been up against powerful European coalitions and deep within hostile territory. If the Ummayads had won against Charles "Martel", they'd have been facing a lot of enemies anyway as well. It's not like "Western Civilization" (and it's an exercise in futility to try to define that) was an entity that posted all its forces to fight a single decisive battle against them evil Orientals.
But such nuances are lost on xenophobes and nationalists.
(Disregard the "Orientals" on the bottom. I can't scroll down to delete it. Posting on a Kindle Fire is a pain!)
Orientals