LIMA, Peru — Wilfredo Saavedra, a former Marxist rebel, led a convoy of some 300 activists from Peru’s northern sierra, wearing an anti-mining T-shirt and Cuban baseball cap. Jim Chomicz, 70, from Birmingham, Alabama, flew here with a church group to learn more about melting glaciers. But for many of their Latin American counterparts, it is all about toppling capitalism, which they blame for the environmental degradation. “Capitalism is the creator of all of these changes to the climate,” said Mr. Saavedra. At a march this week, Ibis Fernández, a Peruvian union leader and organizer of the People’s Climate Summit,...