by teaching that Muslims and Christians worship two different Gods.
Wrong.
CCC 841 The Church’s relationship with the Muslims. “The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us they adore the one, merciful God, mankind’s judge on the last day.”
Given the choice between the teaching of the Magisterium of Holy Church and an organ of right wing propaganda in the service of Americanism, listen to the Magisterium. That way, you don’t wind up embracing the absurdity of polytheism just to keep from acknowledging the things Christians, Jews, and Muslims have in common.
For a non-dissenting take on the common sense of the Church, go here and here.