MadeInGermany is right: You need to sort on the entire year; not just the last two digits. But, it isn't a year 3000 problem, it is a year 2100 problem.
Also note that there is no need to sort the month and day separately. So, you should probably change the sort command in your pipeline to:
LC_ALL=C sort -k 2.6,2.10 -k 2.1,2.5 -k 3,3 file
The following would also work, but I prefer to keep the sort keys distinct to avoid confusion for someone trying to read your code later: