Three foreign soldiers, including two Britons, were shot dead by Afghan security forces personnel on Monday in the latest round of insider killings that have raised deep concerns about the reliability of NATO’s local allies and their ability to keep the peace.

So-called insider attacks have mounted recently as tension between Afghanistan and its foreign backers rises over a series of incidents, including the burning of Korans at a NATO base and a massacre of 17 villagers for which a U.S. soldier has been charged. . .