Constitution > Federal > State > Local
That hierarchy only applies on issues expressly detailed in the Constitution. On most
issues, the order should be Constitution > Local > State > Federal. Most people don't realize that this is what the founders intended.
I think you may be conflating what rights are allowed to be prohibited with what is allowed to be established. Anything is allowed to be established at the local level and up if the constitution doesn't forbid it, but if the constitution says you have free speech or freedom of/from religion, that trumps all laws restricting that freedom all the way to the local level. I.e. if the constitution says you can't have a christian government, not only does that mean you can't have a federal christian government, but that even local town governments can't be established by a church. I'm all for states having rights to decide how they operate, but not for states to make their own decisions to restrict rights otherwise protected by the country as a whole. USA went to war to finally settle that issue.
Whoa. The Constitution does not say you can't have a Christian government. It simply dictates the separation of church and state. This was not only to protect religious liberty; the main reason is because our founders had seen the corruption that the churches, especially the Catholic Church, had brought to Europe. Most of our politicians claim to be Christians, so in essence we do have a Christian government; just not a church government. I think that's an important distinction to make. However, there are town governments run by religious organizations: Omish settlements, Mormon towns in the midwest, and Native American reservations (a special case, but still relevant).
As for state's rights and the Civil War/ reconstruction: I think that the Civil War did more damage to America in the long term than most people believe. Lincoln, while an exemplary politician and a man of admirable character, unintentionally helped cause a distortion of how our federal government interacts with the states. In his days in Congress, Lincoln was a strong advocate for the 10th amendment, and had a very moderate stance on slavery; he opposed it, but thought that the best course of action would be to let the states get rid of it on their own, with limited federal involvement. These were tense times, however, and unfortunately Lincoln's only option in his presidency was to exert a lot of Federal power. Of course, he did this in order to preserve the Union, but it had the unintended consequence of increasing the federal government's power disproportionate to the states from what the Founders intended. We've seen increase in power occur with all of our national crises: the entitlement programs of the Great Depression, the hysteria created during the Cold War, and the Patriot Act (etc.) in the modern era. If we do not return the power to the states, America will suffer the fate of all past empires by restricting liberty and abusing power.