Answer :
"He persuaded leaders to pass an order forcing employers to stop discriminating against workers on the basis of race" is the best option for how Mr. Randolph helped further Civil Rights goals.
I believe the answer is: He persuaded leaders to pass an order forcing employers to stop discriminating against workers on the basis of race.
A. Philip Randolph was a known civil activists which predominantly fight to improve the quality of living of African American Labour workers. His activism revolve around massive wage and discrimination toward African American workers in defense industries during world war II.