The article is actually about how any thinking person can believe in the Catholic Church anymore. That is a perfectly valid question, and I have no objection to anyone asking it. And nothing in particular will happen as a result of the Times's having done so.
Just imagine the outcry, however, if the Times had run a piece asking "Can reflective and honest intellectuals actually believe in Islam's teachings?" There would have been outraged complaints about "Islamophobia" at the Times; claims that the Times was fostering a climate of suspicion and violence against innocent American Muslims; indignant, arrogant and self-righteous pieces in Salon and the Huffington Post written by young Muslims who assured the Times and the world that they were perfectly reflective, honest, and intellectual, and that the Times was "racist" for even suggesting that reflective and honest intellectuals might have a problem with Islamic teaching, combined with weary charges that the Times, like most non-Muslims, harbored bigoted "misconceptions" about Islam. Chris Matthews would mutter darkly about right-wing forces at the Times, and Jon Stewart would mock the Times for its hidden racism and bigotry. Reza Aslan would appear on Stephen Colbert's show to joke about how the Times thinks all Muslims are ignorant savages, and blame Pamela Geller for the whole thing.
But don't worry: none of this will happen, because the Times would never dare to be so "Islamophobic" as to ask such a question about Islam.