Can we tell employees not to talk about their pay with each other?

Generally, no. The National Labor Relations Act (NLRA) grants all non-supervisory employees (not just those in unions) the right to organize and engage in “concerted activity” for the purpose of mutual aid or protection. Concerted means “in concert,” meaning more than one employee is involved. Activities for mutual aid and protection could include discussions about wages, benefits, treatment from managers, safety issues, and just about anything else that two or more employees might have a stake in.