When I was in Jakarta, I felt it was the most dangerous city I had ever visited.
At the money exchange office, the armed guards locked you inside to conduct your transaction. You had to stow away your currency before they would let you out of the building, and a guard would walk you out to the road - then you were on your own.
Lots of typical city stuff... beggars, drunks, people pissing in random places, etc.
Helps to know which taxi cabs are safe, and which will rip you off.
I was there in the wake of the
1998 riots, and there was still a lot of violence against the Chinese-Indonesians.
It's probably changed a lot since I was there over a decade ago. I'm sure its a lot safer now - have fun.
FWIW: Islam is the dominant religion in Indonesia, which also has a larger Muslim population than any other country in the world.