What part of the Constitution would it violate? Is it unconstitutional to ban firearms when boarding a flight? When attending a speech by the President of the United States? When visiting your spouse in jail?
All of those examples have passed the scrutiny of the courts. Just banning firearms in large groups hasn’t.
Well the only way to get court scrutiny is to gain standing and sue them.
You can infer whether it would pass by past cases.
I rather expect burning man banned it themselves, they get to set the rules for their own event
It’s a federal government mandate, as burning man is on federal land administrated by the BLM.
The Constitution limits what the government can do, not private citizens or corporations.
BLM probably refers to the Bureau of Land Management of the U. S. Dept. of the Interior.