There were (and are) large Christian minorities throughout the Islamic world who didn't develop protestant ideas.
That's true. I assume it's because they associated such ideas with Islam, against which they defined themselves and their religion.
In the West, the Islamic threat was not so immediate, and so pseudo-Islamic ideas were able to spread without prejudice (relatively speaking). As the Islamic threat receded over the sixteenth century, such ideas began to spread faster. This would also explain why Protestantism caught on in the areas of Europe that were furthest away from Muslim territory.