Thousands of civilians and rebels across Syria protested allied airstrikes against extremist militants that continued on Saturday, underscoring the challenge the U.S.-led campaign faces in dealing with complex ties among rival rebel factions.

The attacks are leading to confusion on the ground and new complications for American policy makers, as they try to navigate the tensions between the more moderate Syrian rebels they back and extremist ones.

Many of these moderate Syrian rebels—a linchpin of the Obama administration’s Syria strategy to better train and arm the opposition—accuse the U.S. of excluding them from the West’s strategy on Syria and of undercutting their efforts to oust President Bashar al-Assad. […]