"The Theocracy Brief"?

At the Crime and Consequences blog, which is a project of the Criminal Justice Legal Foundation, there is a post by Kent Scheidegger called "The Theocracy Brief," which takes issue with the amicus brief filed by the National Catholic Reporter in Glossip v. Gross (the SCOTUS case involving Oklahoma's lethal-injection procedures).  Here's the primary part of the post:

Some briefs are just downright weird.  In Glossip v. Gross, the midazolam lethal injection case, the National Catholic Reporter has submitted an amicus briefpurporting to explain the teachings of the Catholic Church on the subject.  I have no opinion on whether what they say is correct.  I know nothing about it.  I do have an opinion on whether what they say has any relevance.  It does not.

Last time I checked, the United States of America was not a theocracy.  Quite the contrary, one of the cornerstones of the foundation of our government was a rejection of the mingling of church and state that had caused such enormous trouble in the Mother Country.

If Islamic teachings say it's okay to behead people,* would that make beheading constitutional under the Eighth Amendment?  Of course not.  So why would the teachings of the Catholic Church have any greater relevance?  Because five of the current Justices of the Supreme Court happen to be Catholic?  I am quite sure all five have the integrity not to let such an argument influence them.

* I don't know if they do, and truth of the "if" is not necessary to the point being made.

As it happens, the brief has an entire section dedicated to explaining why the teachings of the Catholic Church with respect to capital punishment are, or at least could be, relevant to the particular question presented in this case.  It seems to me that Mr. Scheidegger's "theocracy" charge is misplaced.  

Obviously, the Church's teachings as such are not binding or authoritative on the Court when it answers legal questions and, generally speaking, whether or not the Church approves of this or that has nothing to do with questions about what the Constitution says (or doesn't) about this or that.  But, in this particular context, the Court's own precedents and doctrines seem to make relevant "the evolving standards of decency that mark the progress of a maturing society" and so there seems to be nothing particularly strange -- and certainly nothing "theocratic" about an amicus brief that says, in effect, "given that you have told us you are interested in what people think about the matter, here's what a whole lot of us think about the matter, and here's why."