The largest and longest lasting Muslim empire was the Ottomans. During their reign, they divided their subjects up into religious communities called Millits. Each of these Millits had autonomy over their own people. They had their own schools, looked out for their own needs, and most importantly followed their own laws. In other words, Sharia law only applied to Muslims, not Christians or Jews. This was always the practice in Muslim nations before the modern era.
Historically Speaking 