If conception can only happen as a result of an answered prayer, then it is entirely possible that the perceived link between sex and babies will be broken. These people might not even realize that sex causes pregnancy, as casual sexual relationships will probably be the norm. Study up on the Trobriand Islanders for a culture where sex is not directly associated with pregnancy.

On the other hand, if the association remains, it is possible that sex will be even more taboo, since it will now have a certain degree of ritual about it. If you know you have to do two things in order to have a baby, and one of those two things is religious, then the other will take on religious significance as well. How that might be expressed in the culture could vary greatly. I could even see a society in which only priestesses are considered holy enough to give birth, and all children are raised by the church until they are old enough to apprentice with their fathers. This could give rise to a matriarchal theocracy. You would then need to sort out how to deal with women who are not selected for the priesthood.