Johnson v. Levy mandates such an exemption, under the new Tennessee religious exemption statute (a state analog of the federal Religious Freedom Restoration Act). For reasons I discuss in my A Common-Law Model for Religious Exemptions article, I think such state statutes are generally a good idea (though I quibble with their wording), even though I think that the Court was correct in reading the Free Exercise Clause as not compelling religious exemptions as a federal constitutional matter.
Nor can court decisions such as this one be criticized on the grounds that the courts, by granting religious exemptions under such statutes, are overriding the will of the political branches. Rather, they are implementing the will of the political branches, as expressed in the religious exemption statute. Under such statutes, courts are supposed to decide whether some religious exemption requests should be granted, at least in the first instance. And if the legislature disagrees with the ruling, and concludes that such autopsy rules should indeed be applied across the board with no exemptions, it could easily prevent such exemptions in the future, simply by amending the exemption statute to specifically exclude autopsy rules.
Note that, as I mention in my article, religious exemption statutes could be faulted for unduly preferring religious objections over deeply held conscientious objections. But they could also be read as covering both, much as some federal laws (including the conscientious objector exemption to the draft, and Title VII’s religious accommodation provisions) have been so read.
Thanks to Prof. Howard Friedman (Religion Clause) for the pointer.