Forrest Gump is so much a story about the time period, this would be a vastly different movie. I'd say just make a unrelated movie inspired by Forrest Gump, instead of trying to make it a remake and thus give yourselve unecessary restraints.
Would new Forest live through the 90s-20s instead of the 50s-90s?
I'm not sure it'd make a good story. The technology is what changed the world in the past 30 years. The 1960s were a super tumultuous time and make a good sorry.
The events in Forest Gump reflect the book and run from 1951 to 1982.
A modern remake would be more like 82 to 2013 or so. So we can talk about what happened with AIDS, since that was a pretty big point in the first one. We’ve got Challenger, OKC, 9/11, Desert Storm, Afghanistan and Iraqi WMDs. Columbine, Station Night Club, GMO food, Clintons Blowjob, …list goes on.
Basicaly comparing Billy Joel’s “We didn’t start the fire”, with Fallout Boys.
A sequel to Forrest Gump was written by 9/11 happened the day before it was turned in. The writers felt like the movie would be pointless after what happened.