I can’t tell you how many times I’ve had a church record (usually Roman Catholic) in one hand; a civil record of birth in the other hand, and the church record has the child baptized before birth. Why is this?
It’s important to remember that in rural Ireland, the priests went out into the townlands, performed baptisms, and in theory wrote them in the main register upon returning. The key to this is to remember that the priest may be the only one in the parish with a horse. Did the priest write it down upon performing the baptism, or was it from memory. We may never know.
Then came civil registration in 1864. At that point, these same people had to register the births of their children with the local registrar. We all know this often didn’t happen. When they did register a birth, they may not have remembered the date the child was born. Even when they did, be aware that the government began to clamp down with fees for late registration of births. Rather than pay the fee, parents often fudged on the birth date of the child.
While these are reasonable explanations for Ireland, this doesn’t explain why we see the exact same thing in North American sources. Yes, you will see this in American and Canadian records. So just be aware, it’s not just an Irish quirk.