Naturalism self-destructs?

A claim frequently expounded by theists is that naturalism is self-defeating: the claims of naturalism, if true, would prevent anyone from ever knowing that they were true. Anthony Flew devotes a chapter of Atheistic Humanism to this claim.

He quotes J. B. S. Haldane:

I am not myself a materialist because if materialism is true, it seems to me that we cannot know that it is true. If my opinions are the result of chemical processes going on in my brain, they are determined by the laws of chemistry, not those of logic.

Flew says Haldane later repudiated this line of reasoning. Nonetheless, let's try to lay it out logically.

Naturalism is self-defeating, version 1 (NSD1):

1. My opinions are either the result of chemical processes or logical processes.
2. If naturalism is true, then my opinions are the result of chemical processes.
3. Therefore, if naturalism is true, my opinions are not the result of logical processes.

The problem here (Flew points out) is with (1.). This is a false dichotomy: there is no reason to think that the result of chemical processes cannot also be the result of logical processes. It's like saying, "Why trust the output of that computer when you multiply two numbers with it? It's just the result of electronic processes, so it can't be the result of mathematical rules!" The mistake here is that the electronic circuits of the computer have been set up precisely so that they implement mathematical rules. There is no conflict between the physical description (electrons) and the logical description (multiplication).

Flew goes on to say that Popper gave a different version of Haldane's argument.

...if "scientific" determinism is true... we believe it,not because we freely judge the arguments or reasons in its favour to be sound, but because we happen to be so determined (so brainwashed) as to believe it....

Flew elaborates that the question has now become

...whether we could by any means have believed other than we did. Unless we could  we cannot take credit for having, as rational beings, judged that these beliefs are true.

Let's call this

Naturalism is self-defeating, version 2 (NSD2):

1. If naturalism is true, the world is deterministic.
2. If the world is deterministic, then our beliefs are determined by things outside our control.
3. If our beliefs are determined by things outside our control, then we could not have believed otherwise than we did.
4. If we could not have believed otherwise than we did, then our beliefs are not the result of a rational judgment.
5. If  our beliefs - specifically, our belief in naturalism - are not the result of a rational judgment, then there is no rational reason to go on believing in naturalism.

The reader will notice that this is, essentially, a version of the Consequence Argument. The issue of naturalism has become an issue of free will.

Flew appears to accept this version of the argument:

...naturalism is in this way refuted in as much as such a naturalist can be taken, as surely he must be, to be claiming nothing more nor less than to know that his scientifically grounded naturalism is nothing more nor less than true.

I find this sentence confusing and cluttered, so let's redact the unneccessary verbiage:

...naturalism is in this way refuted in as much as such a naturalist can be taken to be claiming to know that his scientifically grounded naturalism is true.

In his Epilogue to the chapter, however, Flew clarifies that this is only the case if the words "explain naturalistically" are taken to mean an explaining away of the phenomena. For Flew, on the contrary,

...explanations of the physical aspects of the behavior of these organisms in terms of physical causes are not necessarily irreconcilable rivals to explanations of other aspects of that behavior in irreducibly different terms.

It seems to me, though, that Flew concedes too much. NSD2 fails on several counts. First of all, Premise (1.) is simply false: our best accounts of the fundamental workings of the physical universe are not deterministic. Secondly, even if Premise (1.) should somehow turn out to be true, the rest of the argument suffers from the same issues as the Consequence Argument - specifically, the fatalism fallacy.

So, I don't see any reason to accept either version of NSD.