The prohibitions would also apply to state and town contracts, grants and training programs.
The bill and others like it have their origins in an executive order signed by then-President Donald Trump that ordered all federal agencies to stop anti-bias training that relies on critical race theory, which Trump called toxic propaganda.
Critical race theory looks at how race has shaped and continues to shape American institutions, from schools to housing to the courts.
The bill has drawn a sharp rebuke. More than 150 people submitted written testimony, mostly against the bill, at this week’s hearing before the House education committee.