Making a Difference
This argument looks a lot better than it is:
Suppose some physical event E is causally necessitated by a certain distribution of physical properties P. Then if P occurs, E is bound to occur as well, no matter what else is the case. In particular, whether or not some non-physical event M also occurs before E will make no difference to E's occurrence. (Perhaps M nevertheless causes E, if E is overdetermined, or perhaps M is causally relevant in some even weaker sense, but at any rate M does not make a difference for E.)
To see the problem with this argument, consider a deterministic world where the occurrence of any event E at time t0 is causally necessitated by the state of the world at t-2 (before t): it obviously does not follow that the state of that world at t-1 makes no difference to E's occurrence.
If M is to make a difference for E, it suffices that whether E occurs depends counterfactually on whether M occurs. The relevant counterfactual situations thus are nearby worlds where M does not occur, no matter what happens with P. But the mistake is not only that we're illegitimately supposed to hold P fixed: if we look at nearby worlds where P occurs but M does not, it isn't clear anymore that E will occur. For causal necessitation is not logical necessitation: maybe the closest world with P and ~M is outside the realm of the nomologically possible.
So that argument is no good at all.
Lewis makes a somewhat similar argument in "What Experience Teaches": that phenomenal properties would in a sense be epiphenomenal because holding fixed the causal role of such a property, differences in its phenomenal character will make no difference to anything else.
Now first, this is true for any intrinsic property: holding fixed its causal role, quidditistic differences in intrinsic character will make no difference to anything else. So on Lewis's own terms, the alleged phenomenal properties are just as 'epiphenomenal' as spin and mass.
Nevertheless, I think there is a sense in which intrinsic properties by themselves really cannot figure in causal explanations: that the window had a certain intrinsic property P explains why it shattered only if it is also known that P plays this and that role in the workings of our world. One might even argue that the intrinsic character actually cancels out in the explanation: what explains the shattering is that the window had some property or other playing this and that causal-nomological role.
Maybe a contrastive notion of causal efficacy would be handy here: let's say that whether p or q (or ...) makes a difference for whether a or b (...) iff there is a counterfactual dependence between the second range of possibilities and the first; that is, which of a,b,... is the case correlates counterfactually with which of p,q,... is the case.
Then if two possibilities p and q differ only quidditistically (by swapped intrinsic characters), whether p or q does not make a difference to anything that does not logically involve the swapped characters. So if there is an important difference in intrinsic phenomenal character between our world, a zombie world and a world like ours except that seeing colours feels the way dental surgery without anethetics actually feels, then which of these possibilities obtains makes no difference to any physical events such as people's behaviour. That does sound odd to me, but I don't see why philosophers who reject conceptual connections between phenomenal properties and behaviour should find it troubling.