Genghis Khan was as brilliant as he was vicious. He was, the military innovator, unifier, brilliant politician, courageous warrior, mass murderer and rapist - a terrible and a brilliant man.
He was neither against muslims nor against Christians. He made pyriamids of moslem heads, of Christian heads in Russia and of Buddhist heads in China. He killed everyone who resisted him and demolished everything that stood in his way. Mongols, similar to Romans, btw, would kill everything - men, children, women, old people, pets, farm animals to spread a terror and convince people that the cost of resistance is much higher than that of submission.
At the same time, concurred people were self-governed, they paid taxes (in slaves and goods), and they were free to keep their religions and traditions. Mongols did commit mass rape and murder, looting and arson. Still, I don't believe they were as terrible as muslims under Tamerlaine.
Could you simply explain Genghis Khan's war conduct as the norm of the time? Probably not completely - he raised terror to a different level. Whoever he was, under his leadership and inspiration mongols rose from an obscure wild feuding tribes to build the greatest land empire the world has ever known.