Constantinople fell in 1453. The East was lost to Christianity at that point and the Ottoman Turks were a unified and dominant force. Crusading was no longer an option. The rift between Catholics and Protestants was not really a significant factor, I think. It was simple reality.
I think it is a reach to imply that the West became “pro-Islam” because of Luther.
True, one could say the schism between the Catholic and the Orthodox were what created a vacuum for islam to thrive. Orthodoxy was the original church, after all, only preceded by the copts who to this day are still defending from islam without the Catholic Pope lifting a finger.
Why did Constantinople get the works?