I dont think we separate religion with state, Indonesians hate secularism
Here our former Armed Force General stated what he has done to the nation is actually his service (Ibadah) to his God and for his after life (Jihad)- President Secretary official Youtube
Here another General saying religion is above state in formal ceremony and in front of Presiden Jokowi. His exact saying is that Armed Force duty is to serve for religion first and then state/nation. As religion and state is actually something that is not in opposite, but in line.
Start from 1.10
We have religious minister that manage marriage in Islam, including Haj and supporting both state owned madrasah and private owned madrasah
This is public school ( own by government ) in Jakarta, and you can see here the first activity at school is reading Quran
We give freedom for private religious thing as endorse by Quran ( there should not be compulsion in religion ), but still in majority our women wear hijab voluntarily