The movie is "The Intruder," also released under the titles "Shame," and "I Hate Your Guts."
It's a potent "message" movie made by Roger Corman. And yes, that's William Shatner driving the Klansmen around; he's the star of the movie -- and the villain. He's basically attempting to whip the townspeople in a sleepy little Southern town into a race riot... for his own profit and amusement. It is perhaps the finest work Shatner has ever done.
The town was real, you see. The extras are all real townspeople. And they thought Shatner was the hero of this movie that was being filmed in their midst. For this reason, the scene where Shatner climbs up on a statue in the city park and whips the locals into a frenzy is particularly disturbing.
In Corman's autobiography, he reports the local cops caught on towards the end of filming, and threw Corman, Shatner, and company out of town under threat of arrest... and they actually had to sneak back to film some scenes!
Even now, this movie would not be shown on TV. It's too volatile, and it points out some of the creepier history going on around the Civil Rights Movement.
I hunted for this flick for YEARS before finding a copy on VHS. Imagine my surprise to discover it's now in the public domain... and can be downloaded for free here: