IN CRAFT BEER, a world lit mostly by hype, sour beers burn brightest. An acquired taste for most but a life's pursuit for a devoted few, sours command long lines and high prices when they appear at bars and shops—which they rarely do.

Behind the fans, collectors and cultish online forums are relatively simple brews that get their uniquely puckering flavors not from boutique ingredients but from humble bacteria more commonly found in pickles, vinegar and rustic sourdough bread....