I'm not a big fan particularly, but went reading old plot synopses online today, trying to reconnect with my scattered memories as a young child watching it. On face this story seems rather similar to The Grapes of Wrath for example... a very poor, yet proud rural family struggling to survive the Depression, their socially inequitable position made clear by snobby relatively wealthy people they encounter, amongst many others struggling as they were. They actively engaged in a socially progressive way with Afro-American and Jewish neighbors, grappled thoughtfully with women's changing roles, and often put themselves out to help those less fortunate than themselves, suggesting a broad social conscience. Wouldn't these characters be best understood as quintessential New Deal progressive Democrats?
Since nobody else has answered this question I will take a stab at it. I do not have any sources to back me up, so this is my own opinion. It also delves into things that have happened rather recently, so it breaks the twenty year rule on this sub reddit.
First off, you are correct in your appraisal of the show. The Waltons were for the most part good New Deal democrats and ahead of the curve on many social issues. The only family member that showed even a hint of racism was the third son, Ben, and that was more anti-Semitism than anti-black racism. Ben was also the most business minded of the seven Walton children and he eventually inherited the family lumber mill.
When the Walton's was aired on CBS, the nation elected Jimmy Carter, who was an evangelical Christian from Georgia. Yet during the 1980s, evangelical Christians and the southern states all became more conservative politically. The fact that the Walton's often dealt with theological or moral issues on the program makes it seem quaint in post 2000 America. Then there is the fact that Cable Networks that promote wholesome family entertainment, namely the Hallmark Channel, ABC Family and a Christian network, (whose name slips my mind) really love this program and NBC's contemporary program "Little House on the Prairie". These three networks allow modern TV viewers to binge watch these shows. I mean, if you are a glutton for punishment, you can watch nine hours of the Walton's and seven hours of Little House, every day, Monday through Friday. These three networks cater to the family values crowd and their overtly Christian message is becoming increasingly more distasteful to main stream secular humanists.
That is why I think the Walton's has been characterized as a politically reactionary and conservative program. It is no longer a prime time program shown on a new-work that also shows such liberal shows as "All in the Family" and "Maude", during an era when a Southern evangelical could win the Democratic party nomination to run for the White House. Thanks to the efforts of people like Jerry Falwell and Pat Robinson, evangelicals and the so called family values voters are firmly in the Republican camp.