The idea of “gut health” entered the personal health world just a few years ago, but it has already become one of the biggest trends in nutrition. The new focus on the living microorganisms in our digestive systems has particularly fueled one fast-growing market for foods and supplements: probiotics.

Are probiotics actually good for us? Over the past decade, U.S. consumption has more than quadrupled, and in the next 10 years global sales are forecast to nearly double. But the most recent research suggests that over-the-counter...