the people who insist 2000 was in the 20th century are the same people who get mad if you use Frankenstein to refer to the monster
So... they're correct?
Technically correct on a purely by-the-book level but incredibly annoying and totally wrong on a pop culture knowledge level. Because some dumbass forgot to add the year 0 when making the calendar we're stuck with it though. Otherwise it doesn't make any sense to group 2000 with 1901-1999 instead of 2001-2099 and anyone with critical thinking skills could tell you that.
By that logic, the years 2000-2099 should be the 20th century.