Index funds have long been ridiculed by active mutual-fund managers. But with index funds outperforming more than 80% of their active peers over the past five- and 10-year periods, and investors pulling hundreds of billions out of actively managed funds and putting that money into index funds, it’s hard to claim that passive index investing produces mediocre results. So a new critique has emerged. It is now alleged that index funds pose a grave danger to the stock market and overall economy.

In August one of the most...