First, what is “religion”? The word has many meanings around the world, far beyond how Americans often equate it with the three largest Abrahamic religions. People usually mean some kind of everyday/mundane expressions or representations of faith in, or past experience of, “numinous” (i.e., somehow going beyond everyday experience) things. The expressions often include traditional concepts, stories, institutions, rules, practices, rituals, relics, statues, images, talismans, etc. To the degree that one actually experiences numinous states of consciousness, it usually is not called religion, but instead is called spirituality, attainments, visions, feelings, trips (if drugs are involved), exploration, or just experience. Religious expressions often have as much to do with mundane things (nationality, culture, history, politics, etc.) as they do with numinous things, and experiences that people call numinous sometimes feature mundane religious elements (e.g., Christians sometimes see visions of Jesus or angels, Buddhists sometimes see visions of the Buddha, etc.). To what degree that back-and-forth is accurate, or is people’s brains/minds constructing what they want to see to some degree, is hard to say. Arguably, like much of science, the mundane vs. numinous distinction assumes a conventionally “normal” or “healthy” human perspective. Some people’s everyday experiences may include what others would consider numinous. Also, what humans call everyday experiences are the result of specific evolutionary processes in land-based environments only on this planet, so other species might consider different experiences normal.
Buddhism is often said by Western scholars to have a philosophical or psychological monastic core, which is similar to (and much more developed than) phenomenology in the West, as well as a more religious pop-culture periphery. People usually encounter the pop-culture periphery first, so get the impression that Buddhism is quite religious. Buddhist bhikkhu(ni)s (monks and nuns) are the people who most often and seriously study, engage, and experiment with the Buddha’s theories and methods in empirical or intellectual ways. Lay (non-monastic) people can be anywhere on the spectrum of more experience- or knowledge-oriented to more faith-oriented. Whereas a monk might only deeply revere the Buddha, a lay person might worship and pray to the Buddha. Like many religions, the pop-culture periphery probably has become increasingly embellished with dramatic folklore, ornate artwork, etc., as non-monastic people have elaborated upon Buddhism over more than 2,500 years. There can be quite a stark difference between a spartan forest monastery, which can feel more like a psychology laboratory, and an ornate city temple, which can feel like a shrine or art gallery. Later forms of Buddhism (Mahayana, Vajrayana, Pure Land, Zen, etc.) seem to have drifted the monastic core in more religious of directions, with the Buddha(s) being made more god-like and salvation-oriented.