A year in Mars is longer than the ones on Earth, so ppl living on Mars would celebrate less birthdays and technically die younger.

Permanently Deleted

Sigh, inyuloda, even our sense of time comes from them.
Or we can switch to a lunar calendar, like the Chinese one, and all be older.

Yes officer, I'm 21.
- The Chinese Calendar
  
  The Chinese calendar year is the same length on average as the Gregorian year, because they have leap months.
  
  The Chinese calendar follows a 60 year cycle of when leap monthd are inserted into the year.
  
  A lunar month is 29 or 30 days long (because it's exactly 29.53 days from one new moon to the next) so a lunar 12 month year is just over 354 days long, which is almost 11 days short of the tropical year. To keep the calendar in sync with the solar year, every couple of years thirteenth month must be inserted into the year.
  
  The year 2020 (4717 in the Chinese calendar) had a leap month between it's 4th and 5th regular month, and this year (4720) there was a leap month between the 2nd and 3rd month.
  
  Generally, there are 22 leap months in a 60 year cycle.
  
  This calendar would have an error of one month every 600 years
  
  The Jewish calendar
  
  The Hebrews have a similar system, inserting 7 leap months in a 19-year cycle (metonic cycle)
  
  This one is even more accurate, drifting away one month only after more than 6000 years.
  
  So these two calendars both have an average year length of 365.25 days, so your age in both of them is about the same as in the Gregorian calendar.
  
  The Islamic Calendar
  
  What you are looking for is the islamic calendar. It is purely lunar and doesn't have leap months. Every year is between 354 and 355 days long, meaning that after 33 years in the gregorian calendar, 34 Islamic years have passed. So no, this wouldn't make that much of a difference with the drinking age in the US, but you could get away with alcohol 8 months earlier that way. Of course, ignoring the fact that most Muslims that unironically use the islamic calendar for everything also don't drink

It is a curious thing - I think for the foreseeable future, we'd likely still track age via Earth years for the sake of avoiding this kind of thing. I wonder if/when we do colonize, how long would it take for the Martians to actually switch. How much would our cultures have drifted by that point?

And a related shower thought - until relatively recently (late 1960s), any definition we used to track time has been crazy localized to our planet, compared to other things in math and science where many of those concepts would still work the same elsewhere

A lot of science fiction writers try to address the problem of time when humanity becomes a space-faring race. Star Trek has the idea of a "Stardate" and instructed the script writers to just fucking make it up,

For example, 1313.5 is twelve o'clock noon of one day and 1314.5 would be noon of the next day. Each percentage point (sic) is roughly equivalent to one-tenth of one day. The progression of stardates in your script should remain constant but don't worry about whether or not there is a progression from other scripts. Stardates are a mathematical formula which varies depending on location in the galaxy, velocity of travel, and other factors, can vary widely from episode to episode."

Meanwhile, Asimov in the Robots / Foundation universe, everyone still uses the idea of a 365-day / 24-hour day "year", even if no one remembers Earth (except a R. Daneel Olivaw and a few others).

And Kim Stanley Robinson in his Mars trilogy does what OP notes -- Martian years are longer, and the societies diverge pretty rapidly, within a generation, for a whole host of reasons.
- When I was last working on sci-fi writing (for a game I was running), I came to the conclusion that most places that are in contact with galactic society (in a setting with FTL travel and communication) would probably have one calendar that is standardized for official use, and at least one that is local to the planet. Systems with multiple inhabited worlds might have a system-wide calendar in addition to the individual calendars.
  
  On the other hand, people living on ships, space stations, or remote outposts might track everything in standard time.
  
  Dealing with characters who negotiate contracts across interstellar distances and frequently move between ships and planets made keeping track of things like "what time is it planetside if we rest for 8 standard hours on the ship?" and "if we agree that this contract in another system begins in 30 standard days, but we're occupied here for another local week, how much time do we have for travel?" enough of an annoyance that I went looking for a program that could automatically track these things, but I don't remember if I ever found one.
- Whoa, that's fascinating. Thank you for all the great book recommendations!
I think for the foreseeable future, we'd likely still track age via Earth years for the sake of avoiding this kind of thing

This is actually how it's handled in the science fiction universes. Star Wars for example uses Corusant time as the standard across the galaxy.
- Belters in the expanse are bitter at their colonial ancestors for dictating how they measure time and space