I'm writing a novel, one set in a early-mediaeval world, built heavily upon mythology, involving demons, jinn and wizards. In this world there are mainly city-states, although an empire of horsemen warriors (pretty much the Mongols just unnamed) do exist. When people fight, they use swords and arrows, and it is Middle-Eastern(ish) culturally, with Islam, "Lambs of the Christ-Son"(Christianity) and Judaism existing, as well as the mainstream religion which worships The Grand Goddess. Are similes and metaphors that relate to the time and culture of the West going to seem out of place?
Depends on what you define as "The West". At the period of history that your story references there were European tribes still getting settled, the Saxons and the Franks and the Normans and the Teutons and all that, and then you had the Slavic races and civilizations to the northeast, which would have included the Mongols at some point. To the southeast was Muslim culture which was spread around the Middle East, North Africa, and in the southern part of Spain. In the central south along the Mediterranean was the remnants of Grecco-Roman culture, which I suspect is your drawing point for "The Grand Goddess" worship. (It is pagan in nature, no?) At any rate, you will want to do some research on that period (Pretty much everything after the death of Christ to the mid 1600s) to find how those cultures would have interacted and what their mythology was like. As for similes and metaphors seeming out of place, it will only seem out of place if you can't give the remarks context. If you couch them in your history and give reasons for why they are saying these things, then it won't be out of place at all.
My view is that you should use metaphors and similes appropriate to the story you're telling. You're writing an early-medieval story; you would not say your hero is "putting the pedal to the metal" because that's a car metaphor, and cars don't exist in your world. The imagery you use affects the picture your reader has of your world. If you use metaphors and similes appropriate to your world, you strengthen the image of your world in the reader's mind. If you use imagery that is not appropriate to your world, you are destroying your world in the reader's mind. Don't use imagery that doesn't fit in your world.
One bugbear... As an archer Make sure people loose arrows, or shoot a bow. Never say 'fire a bow' as the verb 'to fire' comes from much later.