Your question would deserve a long essay. R.C. Lewontin wrote a book ("The genetic basis of evolutionary change" - Columbia U.P) on this subject in 1974, right after the neutral theory had been explicitly formulated in the previous few years. The reasons for the controversy over this theory are still alive some 50 years later, despite the enormous advancements in DNA technology. For example the not so hidden polemical tone of this recent paper would not be understandable if some profound ideological issues were not involved; these issues involve something more than "attacks on specific points of neutral theory, (...) or perhaps as attacks on the specific meaning of the term".
In essence, Lewontin argues that the neutral theory has its philosophical roots in the Platonic notion of "ideal" or "type", for which real objects (the genes, in the present case) are only imperfect approximations. This view, applied to the genetic variation in animal species, implies that the role of natural selection is mainly “purifying”, that is, it acts by removing the slightly deleterious mutations that happens continuously and degrade all genomes (when mutations are perfectly neutral, selection does not act at all). As Kimura and Ohta have said, quoting Muller, “the gene through the long course of evolution has finally found itself in man” (quoted in Lewontin, above, p. 30).
The opposite view (can we refer to it as Democritean?) sees all natural populations, man included, as being continuously modeled by unstable and ever-changing environments, so that any attempt to define an “optimum” is intrinsically meaningless. Genomes are highly integrated pieces of firmware, but they are much more fluid, over the generations, than once thought. This means that all genetic variation may have or may acquire meaning, as their molecular or ecological context changes.
Consider an applied consequence of the two views. One of the claims of most anti-racist geneticists is that the variance component among populations of gene frequencies is much higher than the component within populations; this allegedly falsifies the racist argument according to which the differences observed among human population (races) are mostly genetically determined. But if you claim that most of that genetic variation is irrelevant (“neutral”), what remains are the genes responsible for the differences in phenotypic traits, and it becomes obvious that the variance component among populations in the frequency of these genes is lower with respect to the component within populations; and this may be interpreted as supporting a racist view.
It is not automatic that scientists who prefer one theory to the other also support the philosophical implications of that theory. However, the dispute about the neutral theory of evolution cannot be understood without reference to the above conceptual basis.