Bear Butte is a state park. It has been one since 1961, and a National Historic Landmark since 1981, which means a place of continuous active prayer is administered by an agency whose statutory job is recreation. Almost everything that has happened there since follows from that.
Fools Crow v. Gullet
When park officials imposed limits on when ceremonies could be held and how long they could last, Frank Fools Crow and other Lakota and Cheyenne plaintiffs sued under the First Amendment and the American Indian Religious Freedom Act of 1978. They lost in the district court in 1982, lost on appeal, and were refused a hearing by the Supreme Court.
The case is the standard citation for what was wrong with the 1978 Act. It declared a federal policy of protecting Native religious practice and created no cause of action to enforce it, a statement of intent with nothing behind it. That gap is why Congress had to legislate separately and specifically for peyote in 1994, and it is the reason later sacred-site claims were brought under the Religious Freedom Restoration Act instead, where they have mostly failed for a different reason.
What the nations did instead
The pressure at Bear Butte turned commercial. The Sturgis Motorcycle Rally brings hundreds of thousands of people to within a few miles each August, and proposals for bars, campgrounds and a shooting range near the mountain have had to be fought one at a time, each on its own permit.
So the nations changed tactics and started buying. In a series of purchases between 2016 and 2018, the Northern Cheyenne, the Rosebud Sioux and others acquired land around the butte outright.
Buying back land you already hold sacred is now the most reliable form of sacred-site protection in the United States. Not because it is just, it requires a people to pay for what was taken from them, but because a deed does not depend on a court agreeing that your religion counts.
The mountain is in use. The prayer cloths and tobacco ties along the trails are offerings left by people who are still there, and the standing request to visitors is to leave them untouched and to keep quiet.