I'm reading The Palestine-Israel Conflict: A Basic Introduction by Gregory Harms and Todd M. Ferry, and it says this:
After Genghis’s death in 1227, one of his grandsons, Hulegu, decided to move the conquest further west with the intent of driving his forces all the way through the Middle East as far as Egypt. In 1256 Hulegu ploughed through the territories of Iran, Iraq, and Syria. By 1258 the Mongols had reached Baghdad and laid waste to libraries, mosques, and centuries worth of physical history. Estimates vary, but it’s safe to say that a million people were slaughtered during the siege (though Christians and Jews were spared).
Is this the case, as far as we can tell? If so, why did Hulegu choose to spare Jews/Christians?
I'm not an expert on this subject by any means, and if you're interested look into books by Dr. Timothy May. He was a teacher at my college and he's a leader in Mongol history.
But to try and answer your question, the Mongol's tended to not kill for no reason. Only if they had beef with you would they massacre everyone. If they felt insulted by the Muslim rulers, they might spare non Muslims in the area since they were viewed as different people.