"Orthopraxy" basically means "right action" and "orthodoxy" basically means "right belief/opinion." In ADF we have emphasized this distinction to show how our religion is different than religions that are tied together through common beliefs.
A religion that relies on orthodoxy to tie its members together (such as the "Big Three" and many new religious movements as well) can have many different practices that seem entirely unrelated to each other, but are unified by a single belief system. This also results in people who have different beliefs about the way the cosmos works, or about specific key ideas.¹ This leads to conflict in many cases, and a long history of religious warfare bears this out.
A religion like ours, which tends to rely on orthorpraxy, will have specific rituals, orders of ritual, liturgical conventions, and shared symbol sets, but does not need to require anyone to believe anything specific. It is the opinion of orthopraxic religion that it is the sacrifice that is important, not the belief behind the sacrifice: this is less a religion about "why do we do it," and more a religion about "because this thing is right, we do it."
This isn't a modern idea: the Vedics are a clear example of a strong emphasis of practice over belief.² Like the Vedics, ADF has always emphasized things like how to do a ritual over the reasoning behind them. The interesting thing is that right practice tends to bring out shared beliefs.
When we stand in a ritual, we create the cosmos in the same ways that others have before us: we build a sacred center, connect it to all the worlds, and deal with the spirits as individuals with whom we may forge relationships. I like to call these things "ritual assumptions," without which our rituals would not work: we must assume that the gods are individual, that they can hear us, and that the fire is a gateway between the worlds in order for our rituals to go anywhere. Importantly, we must have (at least general) agreement that these assumptions are true during our rituals.
What ends up happening is that, as the ritual progresses, our assumptions "line up" as a community that worships: we generally agree that the conventions of ritual are the realities of the cosmos, and in so doing, we find that we all believe the same things. While at the end of a ritual, we all go back to our own worldviews and our own opinions about the gods and goddesses, we have, for the briefest of times when we stood in ritual, found common ground, and participated briefly in an orthodoxy which arose out of orthopraxy.
¹ - Discussing Pagan Theology - Ian Corrigan.
² - Where's the Belief? Piety in the DP - Michael J Dangler