How about Christianity has the bloodier past while Islam has the bloodier present?”
Because it isn’t true.
That's not even true. It's only the sort of racist, "Euro-centric" bias that leftists love to deride in other contexts that gives that impression.
The Sunni-Shi'ite wars down the centuries, the Mohammedan conquest of India, and Tamurlane's wars collectively slaughtered far more human beings than all of the "Christian" wars and pogroms, even leaving aside the dead from the initial expansion of Islam, the Middle Eastern slave-trade, the Muslim-on-Hindu violence at the time of Indian independence and intermittent anti-Christian and anti-Jewish pogroms that have afflicted those living under Muslim rule.
The problem is, Americans, by and large, are historically ignorant, and to the extent that they know history at all, it's American history and Western European history (with an occasional sneering reference to Russia and central Europe thrown in). They know about the Crusades, the Spanish Inquisition, the Thirty Years War and lesser European wars of religion, the Atlantic slave-trade, and the European conquest and settlement of the Americas (and maybe the Black Hundreds if their school's curriculum took long enough in sneering at Russia).
The sea of blood that is the history of Islam is completely unknown to American liberals (and was to most American conservatives until 9/11 obliged us to start paying attention), along with the rest of world history.