Categorical demands in action are a feature of any social contract, whether through law or religion. It is almost tautological to say that "a person within a group must conform to norms set by their group".. What is there to "the group", if it has nothing binding it? The rules of secular society fit this requirement, regardless of whether their origin is in a theological society.
Within experience, there is no thing for which ultimate evidence can be gained (can the limit be defined?). A hypothesis test with a 0.00% significance level is unattainable if the population and sample size are different (if they are the same, no new information is gained).. In this way, the scientific method does not answer to any Ultimate either - its validity cannot be 100% proven by itself after all. The secular world is still stuck as substantively similar to the religious world.
Moving away from whatever "the ultimate" may be defined as, within the conventional world religion is subject to analysis and change. It would be fair to say that a reasoned approach to evidence is hindered within religious thought due to an established and generally unchangeable metaphysical belief, but Judaism today is not Judaism during the first temple period. Islam today is not Islam before their philosophy touched Aristotle. Again, no different essentially from the non-theist world.
What world-view does not have a metaphysical position? The common sensical hides a metaphysical position, the irrational hides a metaphysical position. Any interpretation of Quantum Mechanics rests on some ontological and epistemological world view.
When you create any theory with a positive metaphysical position, in that you literally have to go "beyond" physics, you find yourself beyond a-posteriori thought, beyond the hypothesis test - beyond the scientific method. If you use reason to attempt to deduce a positive characteristic of Being a-priori, reason will negate it. But if you state that "metaphysics does not exist", reason guides you into contradiction again. The dialogue of Parmenides exemplifies this problem. The presence of a metaphysical position is not the presence of religion but the presence of human thought and language, which in its relative bluntness, creates something out of no thing without even a second thought.
You could choose to drop metaphysics, as the scientific method does (the method does not "create" any ideas of itself, it only strips away unreasonable a-priori hypotheses)..
Nagarjuna did this for Buddhism too however, arguably "neti neti" (not this, not that) for the definition of Brahman within Hinduism does something similar, as does Tawheed in Islam and Tao within Taoism. The metaphysical is not connected to religion (or any thing at all really - it is beyond all that experience offers). In that it is beyond experience, it is the realm of faith - there is no religion within saying "All is One". Metaphysical positions in and of themselves cannot provide rational and complete rule-sets for the physical world. Religion (more broadly ideology) appears when it is said "All is One, and that One is X". X will not stand up to reason because the conventional world is perceived to be relational and not essential - from some frame of reference within experience, X will not be.. When ideology and experience stand opposed and the ideology is followed, that is religion. When they stand opposed and experience is followed, that is the scientific method. When there is no ideology?
Central beliefs that do not Ultimately answer to evidence and reason (or any aspect, however defined, of the Ultimate) cannot provide ultimate answers to the human condition. Any answer to the question of suffering can be sufficient from some frame of reference. To say that the theist fares better at this than the non-theist, is to assume that a theist has a better understanding of the metaphysical world, but "understanding" is meaningless here, as it is a conventional, physical notion. Again no substantial difference between the theist and non-theist position is visible.