What is the anime that is set in the most distant future of today? A lot of anime set in the distant future doesn't specify the calendar year, so it ends up with something like &quot;Before the...&quot; or &quot;XX years ago&quot;.
Some of the future-themed anime such as Gundam and Dragon Ball have their own calendar era which is Universal Century and Age respectively. We can't convert or compare the alternate calendar of the Anime to our real-life Gregorian calendar, so it might be helpful if the Anime has a similar calendar to ours.
According to my research, Legend of the Galactic Heroes is the anime that is set in the most distant future as of today, in AD 2801.
Looks like Legend of the Galactic Heroes is the Anime that is set in the most distant future (AD 3596). You can squeeze it in or append the list if you found any Anime that is set in the era between the Anime(s) or further.

Blue Gender
Yuji wakes up from cryogenic sleep in 2031 and the story begins.

Evangelion 3.0
The events of Evangelion 3.0 occur in 2032, 14 years after Evangelion 2.0 (Assumed in 2018).

Ghost in the Shell: S.A.C. Solid State Society
The most distant timeline in the series take place in year 2034.

Guilty Crown
The main story starts 10 years after the Lost Christmas incident on the Christmas eve in 2029. So it's 2039.

Voices of a Distant Star
The story begins in 2047.

Freezing
In 2065, Earth is in the middle of a war with extra-dimensional aliens called Nova.

Psycho-Pass
The main events of the first two seasons of Psycho-Pass span the years 2112-2114.

Infinite Ryvius
Set in the year 2225, mankind has spread from Earth to inhabit nearly all the planets or nearby moons in colonies and settlements.

Lily C.A.T.
The year is 2264 when the space exploration begins for the main cast.

Gundam 00
The series is set in 2307 AD. Gundam 00 is the only Gundam based in the AD/CE timeline.

Expelled from Paradise
Set in the year 2400 AD.

Cyber City Oedo 808
Set in the year 2808 in the city of Oedo (Tokyo).

Legend of the Galactic Heroes
Set in 3596, Space Era calendar replacing the Gregorian calendar, with 2801 AD now being SE 1.