SAMPANG, Indonesia — The problems began shortly after Tajul Muluk, a Shiite cleric, opened a boarding school in 2004. The school, in a predominantly Sunni Muslim part of East Java, raised local tensions, and in 2006 it was attacked by thousands of villagers. When a mob set fire to the school and several homes last December, many Shiites saw it as just the latest episode in a simmering sectarian conflict — one that they say has been ignored by the police and exploited by Islamists purporting to preserve the purity of the Muslim faith.