Yes, the stock market in The United States is open on Indigenous Peoples' Day, Monday, October 10, 2022
Indigenous Peoples' Day also known as Columbus Day, First People's Day, Native American Day, or National Indigenous Peoples Day is considered a federal holiday in the US. Indigenous Peoples' day honors this history and culture of Native American peoples. In 2021, President Biden recognized the holiday by signing a presidential proclamation. The holiday falls on the same day as Columbus Day which honors Christopher Columbus. In 2022, Indigenous People's day falls on Monday, October 10. Even though banks are closed on Indigenous Peoples' Day, in the US, the United States stock markets are open with normal trading hours.
Source 1 - https://www.nyse.com/markets/hours-calendars