Ms. Manthay and the other uninvited settlers are part of the Landless Workers Movement, perhaps the world’s largest Marxist-inspired movement operating within a democracy and, after 40 years of sometimes bloody land occupations, a major political, social and cultural force in Brazil.

The movement, led by activists who call themselves militants, organizes hundreds of thousands of Brazil’s poor to take unused land from the rich, settle it and farm it, often as large collectives. They are reversing, they say, the deep inequality fed by Brazil’s historically uneven distribution of land.

While leftists embrace the cause — the movement’s red hats depicting a couple holding a machete aloft have become commonplace at hipster bars — many Brazilians view it as communist and criminal. That has created a dilemma for the new leftist president, Luiz Inácio Lula da Silva, a longtime movement supporter who is now trying to build bridges in Congress and the powerful agriculture industry.