Naturalists debate when and whether the death penalty is moral or useful, but all accept that our conclusion must follow from what the actual facts are. Morally, most naturalists accept that killing criminals can be justified in specific circumstances. For example, there is rarely any moral objection raised to shooting armed gunmen to stop a rampage, or gunning down convicted murderers who are attempting to escape from prison. But many naturalists conclude that killing a prisoner merely to effect retribution is useless or even immoral.
All punishments should obtain some material benefit greater than the punishment itself. Otherwise they cannot be morally justified. Reform of the criminal and correction of their wrongs are the most desired ends of sound punishment, with deterrence and self-defense a close second. But mere retribution serves no valuable purpose. Moreover, the degree of benefit must be commensurate with the extremity of the punishment, and punishments that cannot be corrected (if found to be awarded in error) are the most extreme of all. Death cannot be reversed, and is therefore the most extreme punishment. It should therefore confer the most extreme benefits. If it doesn't, we shouldn't do it.
Examined in the light of utility, the death penalty appears to have nothing to commend it. By and large the evidence indicates that execution has very little effect, and is certainly far more expensive than its proposed benefits are worth. Evidence is also mounting that an unacceptably high number of innocent persons have been and are still being executed. Accordingly, there seems to be no logically or factually valid reason to support the death penalty.
For every person we execute in the United States, we must set free ten violent felons for lack of funds to imprison them. Since the net benefit of increasing by ten the number of violent felons removed from society far outweighs any of even the most optimistically imagined benefits of the death penalty, there seems to be no rational basis for supporting it. And since reducing the cost of enforcing the death penalty by ten will necessarily increase the number of innocent people killed by it, a result that is both morally and pragmatically unacceptable, those we consider so dangerous and irredeemable as to justify killing them we should instead imprison for life, and even subject to forced labor to compensate society for the harm they caused it, a fate that will have at least as much, if not more deterrent effect. After all, a lifetime of forced labor is in actual fact far more awful than dying.
In a naturalist worldview, anyone who disagrees would have to argue from actual demonstrable facts that the death penalty does any good that is worth all its costs.