Are Protestants to blame for church divisions?

Yes. And so are Catholics.

"'However, one cannot charge with the sin of the separation those who at present are born into these communities [that resulted from such separation] and in them are brought up in the faith of Christ, and the Catholic Church accepts them with respect and affection as brothers ... All who have been justified in faith by Baptism are incorporated into Christ'" (CCC 818); they are our "separated brethren."

"Christ's Spirit uses these Churches and ecclesial communities as means of salvation, whose power derives from the fullness of grace and truth that Christ has entrusted to the Catholic Church" (CCC 819). The Protestant limbs that broke off from the Catholic tree can still have enough life-giving sap (God's truth and grace) from the root (Christ) through the trunk (the Catholic Church) to be the means of salvation for their members. The Church of Christ "subsists in" (CCC 816) the Roman Catholic Church most completely but not exclusively.

Catholic Christianity:A Complete Catechism of Catholic Beliefs based on the Catechism of the Catholic Church by Peter Kreeft