Martin Luther recognized the tie between them. He spoke of it often enough for his statements to have been quoted in the book Table Talk.

Catholicism is a fake. The real Christian leadership of the Church of Rome left with Constantine when he abandoned Rome to move his capital to Byzantium. The Arian Gnostics sacked Rome and installed their own leadership in the church.

The Gnostics created the religion of Islam to destroy the churches around the Mediterranean in much the same way they used the nordic followers of Arianism to kill Christians in Europe. That way their fake would be the only church left.

Their ploy was quite successful, though even today they live in fear of the Jews accepting Jesus as the Messiah, because that would expose them as a fake. Luther and the other reformers did a decent job of that, but the Jews would be much more successful because of their history.