I would not call them secular, i would rather say tolerant. Secular they were not, cause the immams were in the hands of state, as sultan was also the Khalif...
Calling them modern day secular would be wrong. But one of the most secular countries during that time isn't to far from the truth. The Christian Devşirme had a lot of power. Officially the Muslims had power, but unofficially the Christian "slaves" had a lot of power.