Given that we haven't established a shared understanding of secularism we might need to start there. I think you are definely it overly narrowly. Pretty much anything with a none religiously-based governing power and court system is secular IMHO. It doesn't exclude religion from these processes, with a religious majority and a democratic system this would be next to impossible. It just doesn't let religious law (Sharia, Old testament) be the law or religious leaders (Pope etc) be the leaders.