This is relatively easy to do. Christianity needs to win out in Persia, which is not an ASB premise, and then we have plausible butterflies that can prevent the rise of Islam. After all, if Arabia is surrounded by Christian powers, its influence is likely to win out. North Africa was already Christian before the Islamic expansion, as were Syria and Anatolia. Christian expansion into Indonesia and parts of India are hardly improbable if Persia gets converted.
The biggest challenge is somehow making the European bits of the Roman Empire (and, by extension, the rest of Europe) not Christian. I'd like to propose a scenario where the Christian alt-ERE, due to being allied with also Christian alt-Persia, manages to hold onto (or regain) all of North Africa up to Gibraltar, and similarly attempts a reconquest of the European sections of the fallen West. But the fairly autocratic rule from the East chafes in the West (which still contends that, being the seat of the original and real Rome, it deserves primacy). This sparks some kind of revolt, which has a religious component. Essentially, a successor state covering the European parts of the old WRE manages to secede from the ERE, and it embraces some radical offshoot of mainline Christianity as its state religion. Soon enough, said offshoot undergoes a series of further reforms, to the point that it ceases to be Christian, and is effectively as different from Christianity as Islam is in OTL (although presumably in different ways.) This new religion spreads to the rest of Europe, and later to *Russia.
Now we're set. Christianity covers, more or less, the region that is predominantly Islamic in OTL -- but doesn't cover the area that is predominantly Christian in OTL.