It sounds like the ecumenical movement, this promoting of unity regardless of one's beliefs.
Rome is the author of it. This idea of accepting muslims originated with Rome, and is being embraced by some protestants, so they're just following Rome.
Interesting is that even in their catholic catechism their contradictions can be seen...
(Quotes from catholic catechism)
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."[330]
"Outside the (catholic) Church there is no salvation"
846 How are we to understand this affirmation, often repeated by the Church Fathers? Re-forumlated positively it means that all salvation comes from Christ the Head through the Church which is his Body:
Basing itself on Scripture and Tradition, the Council teaches that the (catholic) Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.