The causal closure principle is a doctrine designed largely to explain what a materialistic world-view must be committed to at minimum. In my analysis of what a philosophical materialist, and, I would say also, a philosophical naturalist must believe, there are three doctrines which comprise is:
1) A purpose-free physical level.
2) The causal closure of the physical level.
3) The supervenience of everything that cannot be captured in the language of physics upon that which can be captured in the language of basic physics.
(It gets a little more complicated when you want to bring in timeless entities like numbers, for example, or even sets. However, such entities, if they exist, are irrelevant to how events are produced in the world).
Now causal closure is consistent with epiphenomenalist forms of dualism, according to which there are mental substances that do not cause any effects in the physical world.
Yes, the AFR is an attack on the causal closure principle, in fact one of the classic defenses of it, chapter 3 of William Hasker's The Emergent Self, is entitled "Why the Physical Isn't Closed."
Why should we believe the causal closure principle? Well, for the reasons that are offered for being a philosophical naturalist of some kind. If the physical world is all there is, then nothing else exists.
So yes, my argument from reason is an attack on the causal closure principle. But I was simply trying to explicate what a contemporary naturalist believes.
There are some people who call themselves philosophical naturalists who deny the causal closure principle, though I think that position leads to incoherence.