Umm...

Gone with the wind

Shawshanke redemption

12 angry Men

Psycho

Need I go on? Plenty of films have had much more cultural impact without any sequels.

Literally all of these are adaptations of written works, with many versions across TV, theaters etc. often before becoming movies.

Psycho had a book only a year before the movie and a tv series way after "Bates Motel" and that was a failure. Most if not all of these are only known through 1 movie and not the entire fiction work. No one remembers the 2nd 12 angry Men or the Psycho book for example. What made them cultural phenomenon was one movie and that's it. And that's the point I was trying to make.

And all of them are ancient (different time, different culture, very different industry) and not one of them is an action blockbuster; not particularly relevant comparisons since their impacts would be completely different than a film like Avatar. Films are more disposable entertainment these days; you look back at not just Psycho, but all of Hitchcock's films, and they're all classics, many took a while to gain cultural traction (Vertigo not until its remaster almost 3 decades later); but that's not particularly true about the last 15 years or so - oversaturation? The Internet? Who knows the reason. But usually what makes a film culturally relevant among new franchises is when the sequels or TV series comes out.

The comparison we are really making is the Marvel Universe, which has (probably) thousands of TV episodes spanning decades, and even more comic books. There are films dating back decades.

Much of the backlash toward Avatar was because of the tremendous success it had, and the transition to 3D film which was unpopular among the hipster/1337/hardcore types. Biases developed because those sorts felt the film did not deserve all the success it received. A very similar thing happened to Titanic and it took nearly 20 years for people to start coming around on that one.

The real test for Avatar will be when the sequels will release. It will generate renewed interest in the original film. And yes, it will no longer be comparable to single run films: depending on where additional materials go, it may become more comparable to Terminator, Star Wars, and other similar blockbuster franchises. I know I am not alone on this forum in people looking forward to that time... although, I admit, I am not a fan of superhero films, but I am a fan of science fiction and sci-fi blockbusters - I think I am one of the only ones here who also really liked Interstellar and Blade Runner 2049 - Sci Fi Blockbuster isn't a popular genre unless it is part of an older franchise (Star Wars, Star Trek), or an adaptation (and not always even then).

Maybe I'll be wrong about Avatar, we'll see. I hope the sequels are great, and I think they will be; I haven't seen a James Cameron film I have disliked - and his films that are sequels tend to be better than the originals  -- I know Alien and The Terminator have fans that prefer those ones, but I think far more prefer Aliens and T2; they also clearly had larger cultural impacts than the originals (which, IMO, were already pretty great films, no one else has been able to direct a great sequel in either franchise aside from James Cameron).

I still think Endgame will pass Avatar. Either it will do it because of a boost from Spider-Man: Far From Home or it will do it from a re-release. Either way Disney will want to put "top grossing movie of all time" on every Endgame Blu-Ray box.

How about Inception. Released a year after Avatar, and based on the amount of times it's been ripped off, the amount of times it's referenced in jokes (mostly playing on the word Inception), the amount of times I've heard it's music or sound-effects used in youtube videos, memes etc., I'm willing to say it's had more of a cultural impact than Avatar. That's just one off the top of my head.

There’s no denying it avatar had no cultural impact and it wasn’t that great either,I don’t know how it made so much money, maybe it was the James Cameron name, or maybe because 3D glasses were a thing back then, anyway like mentioned before there many newer and older movies that had much more cultural impact.
But to go back with the topic I think avengers won’t beAt avatar it’s too late now, and if they rerelease it that would be kind of cheating, but in the same way they could rerelease avatar too.

You are assuming they won't do both. 

Exactly. RoboCop, Predator, Alien, and Terminator are good examples. In the Alien and Terminator's case, they definitely blew up larger with the sequel, but they were already popular before it released and already made an impact on culture. Especially Arnold and his "I'll be back." Most kids couldn't even watch those films, yet they knew the characters and lines from the film, as well as bought the toys and dressed up as them for Halloween.

It's got to be almost a decade since I've seen someone have an Avatar toy or dress up as a Navi for Halloween. Haven't heard a single person reference a line from it or even know the name of one of the characters, even if they claimed to like it. No impact whatsoever. The only people who reference that movie without being provoked to either talk about how forgettable it was or how much it made. Yet, somehow, Cameron thinks Avatar sequels are his future. And this is really why it's taken him this long. He has no idea where to go with the story or is searching for some other gimmick to turn a mediocre film into a huge success.

it won't mean anything when it does (as it seems)

this is the real list, and it won't even crack the top3

Highest-grossing films as of 2019 adjusted for inflation

1 Gone with the Wind $3,728,000,000 1939
2 Avatar $3,273,000,000 2009
3 Titanic $3,099,000,000 1997
4 Star Wars $3,061,000,000 1977
5 Avengers: Endgame film currently playing $2,733,401,768 2019
6 The Sound of Music $2,564,000,000 1965
7 E.T. the Extra-Terrestrial $2,503,000,000 1982
8 The Ten Commandments $2,370,000,000 1956
9 Doctor Zhivago $2,246,000,000 1965
10 Star Wars: The Force Awakens $2,215,000,000 2015