Weeks after Minnesota regulators approved the replacement of an oil pipeline that crosses the state, Native American and environmental groups are starting to oppose the project with a similar playbook to a failed effort to stop the Dakota Access pipeline.

Winona LaDuke, who lives 30 miles from the pipeline’s route on the White Earth reservation of the Ojibwe tribe, said three small protest camps have sprung up. To draw more protesters, she is planning a public campaign that includes a concert with the Indigo Girls in Duluth...