These efforts were called "assimilation" - an attempt to persuade American Indians, by law and force if necessary, to abandon their lifestyle and traditions, and become absorbed into white culture. For some reformers, it was well-intentioned (though still wrong); and for others, it was a way to open up Indian land to white homesteaders and mining interests.
Many white Christians viewed Indian dancing as sexually immoral and savage, and so they tried to make such dancing illegal. For example, in the early 1920s, Commissioner of Indian Affairs Charles Burke issued "Circular 1665," and a supplement, with the aim to ban most native dancing (see, e.g., Margaret D. Jacobs, "Making Savages of Us All: White Women, Pueblo Indians, and the Controversy over Indian Dances in the 1920s," Digital Commons, University of Nebraska - Lincoln, December 1996).
In 1934, as part of the overall "Indian New Deal"--largely embodied in the Indian Reorganization Act of 1934 (IRA)--President Franklin Roosevelt's head of Indian Affairs, John Collier, lifted the ban on dancing (see, e.g., "The Flagstaff All-Indian Pow-Wow," Cline Library, Nothern Arizona University). Truth be told, many American Indians had already been finding ways around the ban, but Collier's action ended the official policy - and was part of a broad New Deal effort to let American Indians be themselves. In 2011, the president of the National Congress of American Indians told the U.S. Congress:
"Kill the Indian and save the man was the slogan of that [pre-New Deal] era. The Federal Government did everything it could to disband our tribes, break up our families and suppress our culture. Over 90 million acres of tribal land held under treaties were taken, more than two-thirds of the tribal land base... In 1934, Congress rejected allotment and assimilation and passed the IRA."
Relations between American Indians and the federal government have never been perfect. Indeed, today the federal government largely ignores the severe problems of poverty, unemployment, and suicide on American Indian reservations. But the New Deal was a bright spot. In addition to the IRA (which promoted business, education, and self-government on reservations), and Collier's administrative actions, New Deal work & construction programs helped improve native lands. For example, over 80,000 American Indians enrolled in the Civilian Conservation Corps, and thousands more found jobs in the WPA, improving Indian infrastructure, farmland, morale, etc. Their work was chronicled in many editions of Indians at Work, a publication of the Office of Indian Affairs (today called the Bureau of Indian Affairs).
Imagine if America had never abandoned the New Deal but, instead, built on it; for example, a job guarantee for all Americans. What could another New Deal do for our fellow citizens on reservations? (See, "Where U.S. Unemployment Is Still Sky-High: Indian Reservations," Bloomberg, April 5, 2018.)