The thing about religion is that it takes many forms. What's distinctive about Bajoran religion is that there's actual tangible proof that the Prophets exist, have preternatural powers, and are interested in guiding the lives of the Bajoran people. So Bajoran religion doesn't really claim anything that isn't objectively verifiable; as far as I know, the Bajorans don't attribute the creation of the universe or their own species to the Prophets. Well, I take that back; I think they do believe they go to be with the Prophets after death, and there's no evidence for that being true. Still, for the most part, there's not a great deal of difference between what they believe about the existence and nature of the Prophets and what's verifiably true.
So what makes it religion? Presumably the level of personal devotion and emotional attachment which the Bajorans have with the Prophets, the degree to which they choose to live their lives in service to the Prophets. Similar in a way to Jainism or Theravada Buddhism -- religions that have no actual deities. In those cases, the religion isn't about whether you believe in the existence of something or its role in your creation; it's about your personal relationship with the universe, how you choose to live your life, what values you embrace and for what reasons.
So I'd say the question of Sisko's alignment with Bajoran religion isn't really one of belief, since the existence and goals of the Prophets aren't really in question. It's more a matter of devotion. Sisko engages with the Prophets on a more secular level rather than embracing them on a spiritual one. To draw another analogy, it's sort of like the difference between being friends or colleagues with someone and being in love with them. In a lot of ways, religious devotion is a form of love. Indeed, in a number of religious traditions, this analogy is made directly and even graphically (see, for instance, the devotional poetry written about Krishna). Sisko has grown to respect and trust the Prophets, sometimes grudgingly, but he doesn't love them the way he would if he were really a follower of Bajoran religion.