Clinton would have grown up in a working-class neighborhood in Chicago, as opposed to the rural town of Hope, Arkansas. Chicago offers a full spectrum of written and broadcast media. Hope might only receive one TV station, KTAL, a CBS station at the time, the home of Edward R. Murrow. In early 1954, when Bill was 7-1/2, Murrow televised a half-hour attack on Sen. Joe McCarthy for his anti-communist crusades. By the time Bill was 12, McCarthy was out and the impressions could have been very different in a large market like Chicago, with five TV stations in 1954.
I'm sure that young Bill would still be aware of McCarthy and/or Murrow, who was a widely viewed journalist at the time.
I think if he grew up in Chicago, Bill's politics would be more influenced by his experiences in a Northern city as opposed to the rural South. Either he becomes more liberal, or he still retains his moderate views albiet with a more urban focus.