From the Tar Pit
For that to happen, you need massive disillusionment in the power structure.
Basically the economy has to implode and government, business, and civil society Hoover for too long to deal with it, like now.
You'd have to butterfly away FDR about 1940 and have a seesaw of fungible incompetents in power from then on to bungle our spin-up and entry into WWII to discredit both parties. Not too hard, really.
Imagine John Nance Garner taking over for FDR (shudder) until 1944.
He wasn't Harry Truman by any stretch. Dewey or any other GOP candidate to challenge Garner didn't need to be a ball of fire to seem like a better idea.
Lots of folks from the 1930's and 1940's remembered the battles between labor and strikebreakers and how to organize, so you have plenty of activist cadre for the youngsters to follow or improve upon.
One butterfly of an early FDR exit would be much more labor activism and official opposition of it, creating a much more proletarian outlook on things fighting over a better deal than status quo vs. OTL where most people with a beef went to college to get away from picket lines and punching a clock.
I'd have to look at demographic data, but IIRC the 1950's were when the kids of the Depression got to strut their stuff. They were stuck between the wave of WWI boomers and WWII boomers so they had plenty of opportunities by comparison w less competition for jobs and more support for social mobility in a rising economy IOTL. They knew firsthand what bad times were so nearly anything else seemed like an improvement.
As to a more activist civil rights movement, it went PDQ with MLK pushing it IOTL provoking the Southern powers-that-be to look like assholes on national TV.
All the 1960's activist offshoots of the civil rights struggle, NOI, Black Panthers, SNCC were borne of frustration with the pace of nonviolent change and the perception that the local powers-that-be didn't give a fig for minorities' welfare and immune to moral suasion.
ITTL, you might see considerable synergy between labor and civil-rights activism but it might become a much more repressive and bloody struggle, unless you butterfly away the Red Scare and J Edgar Hoover making labor activism tantamount to treasonous collaboration with the Soviets.
The Red Scare might be butterflied away because I can't see the US participating in WWII in the totally-mobilized way it did OTL, developing the atomic bomb or dealing out the Lend-Lease so freely to the Soviets. Without US and UK R&D to crib from, the USSR might not have developed the atomic bomb until the mid-50's or later and have been so economically devastated that nobody would have taken them seriously as a superpower. A powerful nation that helped bring the Nazis down, yes.
Bonus points for Beria or Molotov successfully removing Stalin from power and ending the paranoid wall of secrecy making them less threatening to the West.
Anyhow, these are my random thoughts for now.