What a pope or ecclesiastical document has to say about Islam thus seems obviously to fall into what, in the post linked to above, I labeled category 5 statements, i.e. statements of a prudential sort on matters about which there may be a legitimate diversity of opinion among Catholics. A Catholic ought seriously and respectfully to consider statements of this category which concern Islam, but is under no obligation to assent to them. Hence, questions such as whether Islam is inherently more prone to generate terrorism than other religions are, whether Islam is compatible with liberal democracy, how many Muslim immigrants ought to be allowed into a country and under what circumstances, etc. are in the nature of the case questions about which good Catholics can legitimately disagree. Even the question of whether Christians and Muslims refer to the same thing when they use the word “God” – and I certainly believe that they do – cannot be a matter of orthodoxy. There is nothing contrary to binding Catholic doctrine in claiming that Muslims worship some pagan tribal deity, even if (I would argue) this claim is false, ungrounded, and too often driven by emotion rather than clear thinking.
(A critic might say: “But hasn’t the Church pronounced on all sorts of non-Catholic doctrines, such as socialism and communism, various heresies, etc.? So why can’t she pronounce on what counts as authentic Islam?” But such an objection rests on confusion. When (for example) Pope Leo XIII condemned what socialists say about private property, he wasn’t saying “Every Catholic is obligated to believe that one of the tenets of socialism is the rejection the institution of private property.” Rather, he was saying “Every Catholic must accept the institution of private property.” His point was not authoritatively to define what counts as authentic socialism but rather authoritatively to condemn certain errors which happen to have been widely associated with socialism and which are at odds with Catholic teaching. If it somehow turned out that socialists don’t really reject private property after all, that wouldn’t affect Leo’s teaching, because the point of his teaching was to tell Catholics that they ought to uphold private property, not to give a lesson in political science about the history and tenets of socialism.)