Socialism and the concept of capital punishment

Is the concept of capital punishment mutally incompatible with a non-state socialist society? That is, a society characterized by mutual ownership of the means of production and cooperavative management of the economy?

I ask because it seems like every socialist movement I look into is opposed to capital punishment not only in practice (which I can understand, as in our current society it is a tool of capitalist oppression), but also in theory. Every socialist society I've seen proposed by a theorist operates around rehabilitatiion for every crime, even murder, a stance I personally do not agree with.

I wonder why opposition to capital punishment (not only in practice, but in theory) is so common among the big-name organizations that identify as socialist here in the United States, and if the idea of capital punishment is incompatible with economic socialism.

I do not intend to start a debate about the morality or feasibility of capital punishment, but I would like to hear your answers to the question of whether capital punishment is incompatible with an economically socialist society.

To be clear, I realize that many state socialist societies have used and still do use capital punishment for a variety of offenses; my question is specifically regarding non-state socialist societies.

I can conceive of no compelling reason why laws derived from theories of retributive justice are incompatible with socialism. I personally endorse capital punishment for crimes of an especially heinous nature (serial killing and rape, child molestation, etc.) and would advocate on behalf of such a criminal justice system even within the context of a communist society.

With that said, there are basically two reasons why a socialist organization would oppose capital punishment. The first is that they are of the quixotic view that transforming humanity's organization of production is sufficient to produce entirely new human beings—incapable of committing violent crimes, devoid of a sense of national identity, and various other absurdities. The second is that they are utilitarian in orientation and are therefore concerned more with the social utility (as opposed to justice for victims) that obtains from criminal law.

I can understand that. While I'm not entirely unsympathetic to a utilitarian viewpoint, I consider reintegrating convicted murderers with society to be a necessary evil at best and thus can't empathize with the idea that such a society would be ideal.

I would also be willing to accept life imprisonment as a "compromise", but there's an argument to be made that, depending on how far we're willing to go to extend the prisoner's lifespan, such a penalty just constitutes a different form of capital punishment, albeit one that allows for a longer period of time for any evidence that might lead to exoneration to be presented.