One of my parents comes from a poor rural area of Europe where well into the 60s, it was normal to have a "real" birthdate & an "official" birthdate. This was because the government only issued birth certificates in the nearby city, and being poor & rural, it took time to get there by bus, etc.
So I have aunts & uncles with real-official birthdate deltas of up to 2 weeks.
I'd imagine that going back to 1900s or 1880s, when travel was more difficult, who knows. Further, it is possible that the office in some of these areas for registering births was only open certain days of month/week, the further back you go, etc.
Maybe they only went into the city on market days when they had other business, on the first Monday of the following month.
Don't discount superstition and people registering births on nearest special days like saints days, etc.
Some of these abnormalities get lost to time. Many of my family didn't realize they had a real-official birthdate gap until 30+ years later when their mother told them.