BEIJING—As news spread earlier this year that China's government had approved a refinery and petrochemicals base near Kunming in southwest China to process crude piped in from Myanmar, a 51-year-old local environmental activist named Zheng Xiejian started disseminating leaflets denouncing the planned project.

Two months later, campaigning by people like Mr. Zheng has ballooned into full-fledged protest against the facility, which is part of a bid to strengthen energy infrastructure in landlocked southwest China and connect...