Wrong, homesteading was available to everyone, including blacks. Most blacks failed to take advantage of the opportunity. And there was nothing free about homesteading except the opportunity. Homesteading was hard, brutal, and dangerous, and not all homesteads succeeded.
African American Homesteaders in the Great Plains (U.S. National Park Service) (nps.gov)
Black Homesteading
The Homestead Act opened land ownership to male citizens, widows, single women, and immigrants pledging to become citizens. The 1866 Civil Rights Act and the Fourteenth Amendment guaranteed that African Americans were eligible as well. Black homesteaders used it to build new lives in which they owned the land they worked, provided for their families, and educated their children. They built meaningful cultural and religious lives for their communities and governed their own affairs themselves—that is, they sought the full benefits of being free and equal citizens.
About thirty percent of black homesteaders filed on federal lands as individuals remote from other African Americans. They had to overcome severe challenges in the harsh climate just to survive. Many persisted and succeeded. They included Oscar Micheaux, who later became a novelist and the first great African American film-maker; George Washington Carver, whose long scientific career and many discoveries while at Tuskegee Institute are justly celebrated; and Robert Anderson, who failed on his first homestead claim but wound up building a prosperous ranch in Nebraska on 2,000 acres