Aceh is strategically located and was long time an important regional trading center and thus became used to people and influences from all over the world. Religion is important in Aceh. It was from Aceh Islam spread out all over Indonesia, even to Malaysia and Southern Thailand. The Acehnese are devout Muslims.
They respect all other religions as long as they themselves are respected. The recent war/fighting in Aceh was purely political and had nothing to do with religion. Sometimes the opposite was claimed in foreign media. In Banda Aceh the main Mosque (Mesjid Raya Baiturrahman) is just a few hundred meters from the Catholic Cathedral and a bit further away are Protestant Churches and a Buddhist Temple.
It is a set of rules for how to behave and dress, for example the head scarf or “Jilbab” for women. It is normally a matter of personal belief; however, in Aceh these rules are now enforced by Dinas Shariat (a government Shariat Authority). The Dinas Shariat was a request from a political elite and supported by Jakarta as they thought it was what the Acehnese wanted. The former guerillas, GAM, never asked for it and it seems that many or most Acehnese are less happy about the system. In some areas the rules are hardly enforced, especially in remote or smaller places like Pulau Weh and Pulau Banyak.
The rules are only valid for Muslims. They do not allow sale of beer, but in most tourist places, beer is allowed for non-Muslims.
It is common to mix up religious rules and traditions. Many traditions are wrongly stamped as religious rules. It is important to respect both. As responsible tourists we must respect the local way of life. Many areas in Aceh are still very traditional. This fact offers a huge opportunity for a visitor to learn about another culture and see something real. However, in order to let the local community to develop in a way they prefer, respect them and try to adhere to the rules. That is a part of eco-tourism and keeps tourism sustainable.