Genetically engineered corn used for corn syrup which is used as a sweetener in food and drinks. Discretely feed to the general population in order to remove the x-gene from said population.
In the United States, cane sugar quotas raise the price of sugar; hence, domestically produced corn syrup and high-fructose corn syrup are less costly alternatives that are often used in American-made processed and mass-produced foods, candies, soft drinks and fruit drinks.
Glucose syrup was the primary corn sweetener in the United States prior to the expanded use of high fructose corn syrup production. HFCS is a variant in which other enzymes are used to convert some of the glucose into fructose. The resulting syrup is sweeter and more soluble. Corn syrup is also available as a retail product.
The Doctor, Zander Rice of Alkali Transigen, says so, and we are shown the corn and entire infrastructure that supports it (The Cornwood company and Auto-Trucks and the corporate farm next to the black family's land). Rice is the son of the doctor of the Weapon X program that gave Logan his adamantium. Rice is the lead doctor on the new Weapon X program, X-23, which Laura is the 23rd test subject of.