The Church encourages such investigation to a point. Pope John Paul II encouraged scientists to investigate cosmological events around the big band but instructed them not to investigate that phenomena itself.
The Church has reformed itself a great deal in the last few decades but the index of prohibited books, the murder of Jan Hus, and other historical events cast your black and white portrayal of Christianity and Islam into serious question. The reaction of some Muslims surrounding the Satanic Verses was unfortunate, but before you take to much personal satisfaction from this I would ask you to remember Aquinas’s teachings that heretics out to be executed by the state. With all due respect, from a historical perspective, you Church’s actions and reactions with regards to criticisms has been less than exemplary.
*With regard to heretics there are two points to be observed, one on their side, the other on the side of the Church. As for heretics their sin deserves banishment, not only from the Church by excommunication, but also from this world by death. To corrupt the faith, whereby the soul lives, is much graver than to counterfeit money, which supports temporal life. Since forgers and other malefactors are summarily condemned to death by the civil authorities, with much more reason may heretics as soon as they are convicted of heresy be not only excommunicated, but also justly be put to death.
But on the side of the Church is mercy which seeks the conversion of the wanderer, and She condemns him not at once, but after the first and second admonition, as the Apostle directs. Afterwards, however, if he is still stubborn, the Church takes care of the salvation of others by separating him from the Church through excommunication, and delivers him to the secular court to be removed from this world by death. (ST II:II 11:3)*
I would hope you do not impart such biased and self gratifying methods of analysis to your students.