This is a point we can argue over quite a bit. However, "state's rights", if even actually supported, is quite consistent with a divide and rule paradigm of governance. After all, if politics are reduced to a microscopic level, it becomes much harder for popular organization to occur and overcome disparities of wealth and entrenched, inherited influence. Furthermore, that's generally about specific policies, not the more general structure of governance. While you can certainly find Freemen and the like loudly decrying the notion of a strong central government, this is considered a fringe position. Conservatives generally advocate a strong military and strong law enforcement; popular rule by the Great Unwashed is to be feared and loathed whether said mob rule is conceived as being by the poor, urban minorities, or coastal DFH. Populist posturing to one side, conservatism often puts forth rhetoric that can be boiled down to praising a "moral, responsible (adult) Us who can be trusted to rule wisely" as opposed to a "fickle, reckless (immature) Them who lack the Wisdom to be trusted with authority".
As to "state's rights", the American conservative movement tends to advocate "state's rights" only when faced with an inability to succeed in applying its preferred policy at the national level... and they're quick enough to champion the primacy of federal regulation when it advances their agenda. Consider stricter emission standards in California, or states deciding to perform marriage w/o gender restrictions, or states legalizing medical marijuana. Or (cringe) Terry Schiavo. Mysteriously, principles of local governance and "state's rights" vanish into the mists. Honestly, this serves as more of a convenient bludgeon than a sacred principle in the modern political landscape.
[e] Also, given that the context is a discussion of origins of political movements in the US, recall that state's rights was originally something embraced by the liberal Jeffersonians in opposition to a nigh-monarchical federal government as advocated by the conservative Hamiltonians. I repeat: in American politics state's rights is quite often a handy bludgeon moreso than a sacred principle.
[e2] Regarding the hoary tradition of populist anti-elitism, recall that the conservative interpretation of it very rarely manifests as resentment of economic elites, but rather of intellectual elites. The simple, jus' folks rich who earned their status by dint of hard work and thrift (and/or inherited wealth and exploiting the masses) are okay because of shared social values (see e.g., rich blue-blood scion with two Ivy League degrees G. W. Bush), as opposed to the fiendish, contemptuous intellectual elites (who may be rich or may be poor) who came by their status through mere schooling and/or snobbery (see e.g., rich blue-blood scion with an Ivy League degree J. Kerry... not that he's particularly Liberal, but that's unfortunately irrelevant to the matter at hand). Reverence for "small town" life has little to do with a preference regarding manner of governance, but it still is relevant to the liberal-conservative dichotomy largely because it's a lingering reflection of the squabble's very Enlightenment roots.