It isn't a religious issue. I think Eeyore has a good point that this has been promoted as part of a population control effort.
That said, some of your facts seem a bit off. I know that in the early 1980s several states had an AoC of 12 or 13, and religious South Carolina and irreligious Hawaii were the last two states in the U.S. to maintain an AoC of 14, into the 2000s. So did Canada. Of course it should be noted that the Age of Consent was never intended to be "permission" to have sex. It was rather a question of who was to be held legally responsible for the crime of fornication, which is to say, the crime of sex outside of marriage. After the sexual revolution in the 1960s it took a while for attitudes about the law to change, but attitudes towards the law were not identical to attitudes towards sex outside of marriage, and neither of these were the same as attitudes about age and sex.
It's hard to trace the origins of all these changes. One of them of course was the anti-religious Jean-Jacques Rousseau, whose rejection of the doctrine of original sin in the late 1700s led to the entirely new idea of "childhood innocence" in the 1800s. Then the "white slavery" moral panic originated in England around 1880, which directly led to the age of consent being raised there - first to 12, eventually to 16 where it remains today. But that was chiefly an attack on prostitution, with attitudes about age only playing a supporting role.