Fortunately, my own ancestors disappear into obscurity just this side of the change in calendar in the UK. Britain, and the territory it governed, changed from labelling dates according to the Julian Calendar to using the Gregorian Calendar in 1752. Wednesday, 2 September 1752, was followed by Thursday, 14 September 1752.
It seems likely that people caught up in this change did not change the date on which they celebrated their birthdays. Christmas Day in the Julian Calendar was (I think) Julian December 25, which nowadays falls on Gregorian January 6. Christmas was celebrated in Britain on the date labelled 25 December in the Julian Calendar in 1751, and the date labelled 25 December in the Gregorian Calendar in 1752. (I’m guessing, here. But I think that’s the case.)
Just as changing time zones has no effect on birthdays, changing calendars probably didn’t either. There were no birth certificates and no picky laws about age back then. However, had there been, someone who had a birth certificate saying “1 Jan 1740” (Julian) would have been able to buy alcohol at age 18 on 1 Jan 1758 (Gregorian), even though their biological maturity would have been 12 days short. They celebrated their birthday, and thus counted their age, on the date marked on the calendar, independent of their biological age. On that day, if asked their age, they would say “18 years and 0 days”.
The unlucky people born on 3-13 September never had a birthday in 1752. I wonder if there were lots of parties held on 14 September 1752, for everyone that missed a birthday?
The birthdate calculator doesn’t take any account of the calendar change. I did remember to stop it accepting dates before 1753. I did plan to add support for Julian dates, but was stopped short when I read some detail about the Julian-to-Gregorian switch. That excellent page reminded me that New Year’s day in the British Julian calendar, unlike that in other Julian Calendars, was March 25. I had quite forgotten that, despite having written code for it in the past. Quite how that changes age-on-date calculations needs some more thought!