One of the possible legal challenges to affirmative action programs is that they violate the clause of the fourteenth amendment. because this amendment is at play, any affirmative action program that uses race or ethnicity as a basis for decision making is reviewed by the courts using scrutiny.

The answer is equal protection clause
According to the equal protection clause, every individuals that located under a same jurisdiction has the right the have a same treatment by law enforcements.
The clause took effect in 1868 in order to make sure that none of the states have the power to discriminate against a certain individual solely because of their superficial differences.