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sorry, i should have picked a lower resolution poster image whoops (e: fixed)
Also holy shit this movie still kicks so much ass. I rewatched it recently and i was blown away by how excellent it still is 25 years later. Most movies do not age this well.
The green is part of why the movie still looks good years later. It hides green screen artifacting. One of the problems with green screens is sometimes they reflect green light onto things, creating an uncanny valley. This is especially a problem with shiny surfaces, like...say....black latex and sunglasses.
The Matrix hides it in plain sight by masking everything in a green filter. Mixed with practical effects, you don't notice when something is CGI or the CGI just looks good (like when the kid bends the spoon in the Oracle's apartment).
If you want to see a movie where green light reflects off surfaces it shouldn't and it looks like shit, in the first Thor movie it's really easy to spot. The Mandalorian has been a major breakthrough because they use a giant ass LCD screen (instead of a greenscreen) that forms half a dome around the set. This allows them to use CGI, but the light is much more natural looking.
I think the worst CGI in the whole trilogy, is when Neo fights the many Smiths in reloaded and even then it's a great scene and you could handwave it as the Matrix failing to render everyone completely due to the strain from what they're doing.
Yeah that looked like shit even when it came out. IIRC it was the first of its kind, though. The software they used was the best available and made specifically for Reloaded. Subsequent films outside the franchise would use improved versions of the same tech, which is why they don't look like garbage.
I do a bunch of green screen photography and editing, if I mess up and there's obvious green reflections I cheat and make it black and white.