English is a Difficult Language

It's really hard, I know.

The rules are simple. Every time a Republican who is a Catholic is asked for an opinion on the encyclical, place him into one of two categories: the Catholic Republicans or the Republican Catholics.

The difference between the categories depends on which term is doing the modifying. A Catholic Republican is a Republican whose Catholicism comes first, whose faith and devotion to the teaching authority of the Magisterium of the church takes precedence when a conflict or tension arises between it and loyalty to the party's ideology, policy platform, and electoral prospects. A Republican Catholic, on the other hand, is a Republican who puts his devotion to the party ahead of his faith...

You've got it exactly backwards. The "term doing the modifying" is the adjective, not the noun. So in "Republican Catholic," you're talking about a Catholic who happens to be Republican. They're the ones who will put their Catholicism first, and their Republicanism will only modify that essential Catholicism. Vice versa for your other category.

Don't feel bad. A similar error is behind a very common misreading of the Second Amendment.