Philip,
''A conservative view would be that temporal causality is fundamental but ontological causality is just reductionism and is not what science is about. I take the opposite view.''
In the reductionist view the universe is just the sum of its parts. However, if particles have to create themselves, each other, so particle and particle properties must be as much the cause as the effect of their interactions, where particles only have a physical reality to each other if, to the extent and for as long as they interact, then the part(icle)s cannot exist without each other so have no autonomous, independent existence. A universe can only be the sum of its parts if particles, particle properties would only be the cause, and not also the product of their interactions, in which case the question as to the why of their properties never can be answered, explained ontologically nor (temporal) causally even in principle.
If the most fundamental law of physics says that what comes out of nothing must add to nothing, then this 'sum of its parts' must be nil (so everything inside of it, including space and time somehow must cancel so it has no physical reality as a whole, as 'seen' from without, so to say), then it obviously doesn't make any sense to make statements about the universe, to assert that it has a particular entropy. Moreover, by saying that its entropy changes in time, we in fact say that the universe lives in a time realm not of its own making, so Big Bang Cosmology (BBC) in fact represents a reductionist, i.e., an essentially religious view on the universe. To speak about the properties of the universe can be justified only if and when the inside objects, their particles, only are the cause of interactions, not when they are both cause and effect of their interactions.
As to ''The arrow of time emerges as a macroscopic effect from thermodynamics which tells us that entropy always increases in one time direction'', no, I still disagree with you, and not only because to do so would presuppose an initial low-entropy state of the universe, something which cannot be explained ontologically nor (temporal) causally. Such initial low-entropy state would make the universe an automaton which, once winded at (or just before?) the mythical bang, only can unwind in a preordained fashion so implies the intervention of something outside of it to wind it up, to provide it with a low entropy in the first place.
If particles cause, create one another, then real particles can be thought of as virtual particles which have managed to set up a continuous energy exchange, which by alternately borrowing and lending each other the energy to exist, force each other to reappear again and again after every disappearance. According to the Uncertainty Principle (UP), the smaller their distance is, the higher the frequency they exchange energy at, pop up and disappear to pop up again and again, the higher their rest energy is, the smaller the areas are where they keep popping up, the less indefinite their position is. It is clear that in this scenario particles owe their existence to each other, that they exist to each other only if and for as long as they keep interacting, exchange energy: as they cannot exist as autonomous, independent objects, the universe clearly is (much) more than the sum of its parts.
The fallacy of reductionism, the flaw at the heart of BBC is that it imagines to look at the universe from without, like we imagine God to look at His creation, so is even worse a 'theory' than creationism which at least is honest in stating that, yes, the universe has been created by some Outside Intervention.
My objection to (temporal) causality is that it confuses cause and effect, or, to be more precise, that, if particles indeed are both cause and the effect of their interactions, we can no longer say that their mass precedes gravity between them, so instead of saying that particles contract because they have a certain constant rest mass (they somehow, mysteriously have been provided with) and gravity is attractive, we can as well say that they acquire mass only if and when they contract (agreeing with the UP), that in doing so they power time, so the ''arrow of time'' has nothing to do with entropy whatsoever. The idea of temporal causality, that cause precedes effect, only would make sense if we could determine what precedes what in an absolute sense, if we could look from outside the universe in, which Big Bang Cosmology (BBC), in the concept of cosmic time, wants to make us believe is justified even though we cannot actually step outside of it. Sorry if this has again turned into a lengthy reply.
Regards, Anton