I apologize for the somewhat a priori answer, but it's because the question feels inherently flawed. You need to specify what you mean by Sharia law here. All Middle Eastern Islamic empires and kingdoms have used what they thought was "Sharia" throughout history, but your question boils down the staggeringly extensive, negotiable, and constantly-shifting compendium of jurisprudence on Sharia to a simplistic singularity. An "it". Many extremist commentators, both Western and Islamic, tend to make this claim that the Quran has a clear and singular interpretation of what "the law" is under Islam. The incredibly broad range of means of implementing a legal order throughout Islamic history have shown that interpretation to be incredibly naive. There are too many unique situations and methods of legal practice that a book of Biblical stories and adulation of God can cover.

Meanwhile the Arabic term for legislation/legality, sharaiya, comes from and barely deviates from the exact same root term - so calling it "Sharia law" in the Renaissance Era context is like calling it "law law". Involving religious authority in judicial and legislative affairs is a deeply-rooted Middle Eastern practice that persists until today even in secular nationalist nations like Egypt, and the idea of separating law from religion in a liberal manner consistent with the modern West would have been novel and unimaginable in the 14th-16th century Middle East.