I think you're misunderstanding what is meant by Sharia. It is not a strict set of rules. Because of this, it is necessarily influenced by ethnic traditionalism. Now if you're looking for western countries which have Sharia courts, the United Kingdom and India are two which come to mind which allow certain civil disputes to be resolved in Sharia courts.
For a Sharia court in the UK to have the power of law though the participants in the case all first have to agree to that though, otherwise they don't have a legal leg to stand on.
So it is only after you've voluntarily agreed to be bound that the court can proceed.
