I really dont see how religion has anything to do with it.
Here you have two species, each significantly more advanced than the species that they coexist with, both fighting for that top spot on the food chain in a very dangerous environment. You could probably throw Smilodon on the lost if you wanted to. Those species who were ill equipped to adapt to the environment and procure recourses essential to survival died out by default. Those who were able to survive on their own then had the other species to contend with. Smilodon was a major threat to early humans, and it stands to reason that they were eradicated wherever humans could find them. Since they both had the same prey population then thats pretty much everywhere. Bye-bye kitty.
You could use the same theory applying it to the Neanderthals. The two species probably competed with each other for just about everything: food, shelter, trade routes, you name it. The difference is that Cro-Magnon man had a distinct advantage when it came to brain power. They were physically inferior to their cousins the Neanderthal, and in a fist fight would probably get ripped limb from limb, literally, then eaten. But Cro-Magnon had the great equalizer - they could make weapons. More specifically, the bow; it would allow them to safely bring down prey, resulting in less injury than with simple spears and stone knives, decreasing death rates due to infection, etc. The bow would also allow them to kill their slope-headed cousins without fear of direct physical confrontation.
Let the Genocide begin.