Maybe I'm a little ignorant here, but isn't Indonesia pretty civilized? And in theory, there's quite a few Islmic countries that have separated state and... mosque (?), like Egypt. BUT no doubt religion is still a VERY powerful influence in all these countries.
Egypt is a militairy state from what I last heard. Turkey is the only real democracy, that's why I used it as an example. As for Indonesia, maybe, I don't know an awful lot about Indonesian politics.