Christian monarchies didn't practice polygamy, which enabled female heirs to become viable candidates. Most monarchies outside of Europe widely practiced polygamy and concubinage, which gave them an ample supply of male heirs to choose from. Women rarely entered consideration as a result. European societies weren't much better toward women, but some kings swallowed their misogyny to preserve their lineage. Likewise, many otherwise opposed nobles would have accepted female heirs, rather than living with the risk of a power struggle for the throne between numerous claimants and the chaos which would ensue. Most Christians, just like Muslims, would probably have considered it decadent and sacrilegious for a woman to rule over men, but even then people had their practical side.
