Joe, defining 'society' is also needed...or not. Never ask for a definition when a chance to be creative might get squished. There are also societies within countries. The Amish are non-secular. We have some around this place who might answer questions on specifics. Native American (Indian) reservations withing the US have their own system of government. I don't know how much religion is involved in that government, but I know that Shamans, medicine men, etc, are respected and consulted by leaders. Other self-governed indiginous peoples may qualify. They may provide a kinder, gentler type of secularism (if they actually fit the definition of 'secularism', and I'm not sure about that) compared to Iranian fundamentalists.

You gotta figure that if everyone in your class has the same assignment, most of them will talk about Muslim fundamentalists vs. western democracy. As a result, the differences may be a lot more extreme than they would be with less extreme secularism. It's easy to find differences, everybody can do it (and will), and they'll be fairly general and impersonal. If you dig deeper, you may wind up with a far more interesting report, both for you and for your teacher. Good luck, and enjoy!