SOSEONG-RI, South Korea—Climbing to a high outcropping in this rural corner of South Korea, a hiker can spot a pair of U.S.-made antimissile launchers parked on a golf course in a forested valley, aimed high over jagged mountains toward North Korea.

The bucolic scene is at odds with the controversy around the launchers, part of a Terminal High-Altitude Area Defense, or Thaad, battery installed here in April amid mass protests and a presidential race in which the winning candidate, President Moon Jae-in, questioned their deployment.

For months, a mix of antiwar Buddhists, university activists and local villagers protesting the Thaad system from a roadside encampment seemed to be gaining the upper hand. After taking office in May, Mr. Moon halted the deployment of four additional launchers needed to complete the battery, pending environmental review.

Then, North Korea tested an intercontinental ballistic missile July 4. Public approval for deploying the system has surged to 72% from around 50% earlier in the year, a recent Gallup Korea poll showed. Mr. Moon gave the go-ahead for the completion of the Thaad battery after the launch on July 28 of a second North Korean ICBM.

These days, only a handful of protesters remain camped in blue tents draped with “No Thaad, No War” along the country road leading to the now-closed golf course where the Thaad battery sits. They have vowed to block delivery of the remaining launchers.