Of course the notion that there is no such thing as the self because it cannot be explained naturalistically or demonstrated by science is the philosophical naturalistic argument par excellence.
Who made this argument and where? There are arguments that the idea of a self is not quite what it seems to be "from the inside" but those are based on more than the assertion of naturalism. There are also arguments that the mind is the direct product of the brain but those are based on actual evidence, not a philosophical position.
The dismissal of philosophical argument as a path to truth is another one...
Who has done this (as opposed dismissal of a particular argument)? And how would that make somebody a philosophical naturalist anyway?
...marked by the insistence of evidence instead and the subsequent suggestion that evidence of course means scientific evidence...
The point here is simply that if you want to introduce some other evidence we need a way to evaluate it. This is not philosophical naturalism, it's just logic.
...and finally the equation of science with atheism as betrayed by continual sidestepping back into science...
Who equates science with atheism? Why would that make them a philosophical naturalist?
...Science does not have anything to say about any philosophy...
That actually depends on the philosophy.
...and leads to facts about a physical world any appeal that equates physics with the word reality. Is a philosophical naturalistic argument.
Asking for a reason to accept the objective existence of things that aren't "natural" is not taking the position that no such things exist and therefore is not philosophical naturalism.