>The basic idea is to solve certain conflicts according to the religion of the people involved, which seems a good idea in principle (Christians being able to apply Christian laws, etc.).
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>The protests have been mainly because Sharia can conflict with women's rights. But the proponents of allowing Sharia for Muslims say that that will not be allowed. In other words, it seems that the applicaton of Sharia would be limited.

A good idea? Not here! Separation of Religion and State (here called Church and State) is a basic idea of democracy. Practice religion at home and Mosque, Temple, Church, not in the Courts. Stoning someone, even though it is OK in the Bible and Koran, is still a crime in any modern country, including Bolivia. Unfortunately not in places like Saudi Arabia, Iran or Nigeria.