Two Anti-Naturalistic Arguments from Value

Here's a plausible (and entirely unoriginal) argument:

1. If naturalism is true, then our capacity for profound aesthetic experience is a mere evolutionary spandrel.
2. Our capacity for profound aesthetic experience is not a mere evolutionary spandrel.
3. Therefore, naturalism is not true.

Motivating (1): If naturalism is true, then we are the product of an unguided evolutionary process. Now, our capacity for profound aesthetic experience clearly does not confer any direct evolutionary benefit (a taste for Bach would not have been terribly useful in Paleolithic times). So on naturalism, our capacity for such experience is merely the accidental byproduct of selection for some other useful trait.

(2) is motivated by the fact that it is very hard to believe that something so central to a good human life as profound aesthetic experience is a mere evolutionary spandrel. That sort of assessment seems to profoundly undervalue such experiences. 

Replacing the word "aesthetic" with the word "moral" in the above yields a second argument of comparable force.