This is a tricky question, and the answer depends on the law. The Americans with Disabilities Act and Title VII of the Civil Rights Act (the federal non-discrimination statute), for example, specifically state that they do not apply to Indian tribes, and therefore to businesses wholly owned by Indian tribes. Some other laws, like the Fair Labor Standards Act, apply sometimes- when a tribe is operating as a “commercial enterprise,” but not when the tribe is acting as a “governmental entity.” For example, the Ninth Circuit Court of Appeals in California has held that overtime laws do apply to a store owned by a tribe, but not to tribal police.
The Second Circuit court of appeals recently upheld a Connecticut Court’s dismissal of a claim arising out of an employee’s termination from Mohegan Sun Casino. Read more here. This employee claimed that she was unfairly terminated under both Title VII of the Civil Rights Act, and the Age Discrimination in Employment Act (ADEA). The court held that because Congress had not expressly made tribes subject to these laws, and the tribes themselves had not waived its sovereign immunity in this context, employees at Mohegan Sun were not protected by these laws.