The truth is not black and white but shades of grey. I'm not classifying the rulers as Anti-Semites- though most undoubtedly were personally- they were just unsentimental, pragmatic. Cynical if you like. It was not out of any love for the Jews or Christians that they protected them. It's not a question of being against or for, but of statesmanship. They protected minorities when it suited them.
The Islamic countries, the Ottoman Empire in particular, were more than happy to take in the Jews because of their wealth, diplomatic/trade links and business acumen. Don Josef Nasi was an influential figure in the Ottoman court during the 1570s, soon there was an influential Jewish lobby, Jewish doctors were employed by the Sultan and Jewish women were favorite companions of the harem ladies. The Empire was probably the most tolerant place in the world at the time.
The common people OTOH would often mistreat the Jews to the best of their ability. There was not much love lost between different groups.
Another reason for the occasional outbursts of violence, was if the ruler thought the Jews were getting too uppitty, he would withdraw his protection and allow violence against them, sort of an "we'll see who's boss here" thing. Happened to Armenians and Greeks too.