Being Islamic is directly related to being a theocracy, therefore the depravity must be related. Personally I think they can be majority Muslim without the depravity if the culture was cleaned up, but that is unlikely because culture binds all these issues together.
The depravity would happen whether the theocracy adhere to Islam or literally any other religion, be it Christianity, Judaism, Hinduism, Buddhism, Sihkism, or ANY religion you can think of.
As I said, it is a culture thing and thus all these issues are mixed together, but you cannot place the blame of Islam.
Also some of those religions are starkly against "depravity" and thus they would have to go against the religion rather than adhere to it. I don't doubt they can be officially Sikh and yet to starkly against the religion in action.