In the end, Roosevelt agreed to Randolph’s request and issued Executive Order 8802, which forbade discrimination in defense industries.Roosevelt did this because

Roosevelt issued Executive Order 8802 to prohibit discrimination in defense industries as the United States prepared for war. Randolph’s planned march threatened to draw attention away from or disrupt those preparations, so Roosevelt acted to address the issue before the march took place. The best answer is “Roosevelt feared any disruption in the nation’s efforts to prepare for war.”

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