In defense of the horse racing theory, one of the best R&C articles ever was Gray Baskerville's June 2001 story, "The Legend of the Car that Raced the Horse: Why the Drags are 1,320 Feet." According to that story, hot rodding pioneer Ak Miller would have told you that "the standing quarter mile became SOP thanks to an unusual race staged between a quarter-horse and Pete Henderson's Deuce highboy" in 1944.
We've even read interviews with CJ Hart, in which he acknowledges the influence of quarter-horse racing. But Leslie Long's recollections from Santa Ana suggest a more random reason. "When they finally started to have standing starts at Santa Ana, the cars had to move away from the fence (where they had previously lined up for rolling starts). The distance that was left was a quarter mile. So it was really an accident there-it just happened to be the length of the runway."
Leslie's version is backed up by an interview with Wally Parks from Westways magazine, published by the Southern California Auto Club (which also sponsors the Wally Parks NHRA Motorsports Museum). In that interview, Parks said specifically that the quarter mile was not from horse racing, but from test runs and races at airport runways. That distance allowed room for the cars to accelerate and decelerate without running out of pavement. Publicity in Hot Rod (edited by Parks) and other magazines helped establish the quarter mile as the standard for drag racing.