Why would Jews be more safe in the land governed by a holy book that exhorts its followers to kill Jews than in a land governed by those whose faith is based on the same God and scriptures as those of the Jews?
I don't know. It may be a matter of interpretation of the Koran. To many Muslims at the time, Jews and Christians were to be allowed to live in peace -- but they weren't allowed to rule. In many cases, it was that the Muslim rulers were more interested in running a successful nation than a strictly religious one.
But the fact is that during the Medieval period and the Renaissance, Jews were generally treated better by Muslim countries than Christian ones.