Should religious doctrines influence Eighth Amendment jurisprudence?

Thanks to this post by Orin Kerr, I took a closer look at this amicus brief filed in the SCOTUS  juve LWOP cases on behalf many religious organizations.  As Orin notes, the "substance of the brief is provocative [as] it argues that religion should inform 8th Amendment jurisprudence."  Specifically, consider these passages from the amici brief (with quotes and cites left out):

The importance of a society’s religious organizations’ views on issues of morality, crime, and punishment to that society’s standards of decency is well recognized.  Indeed, for the vast majority of mankind, crime, punishment, and reform are still inextricably bound up with religious views about sin, judgment, and forgiveness.  There are few, if any, institutions that can claim a greater tradition of working with and studying the conscience of the human person and related questions of guilt, blame, and suffering than those of the religious community....

Amici, as members of the religious community, are uniquely positioned to provide invaluable guidance regarding the issue presented in these cases: whether sentencing juveniles to life imprisonment without the possibility of parole for non-homicide offenses is contrary to contemporary standards of decency and therefore violates the Eighth Amendment’s prohibition of cruel and unusual punishment.  Their religious traditions — Christianity, Judaism, Islam, and Buddhism — have played influential roles in societal discourses about morality and criminal punishment throughout history, and continue to do so today.  An overwhelming majority of Americans continue to rely on the teachings and instructions of these faith traditions on matters of morality and justice.

I am curious to hear reader reactions to the suggestion that religious traditions and teaching might have a special role to play in Eighth Amendment cases.