It is illegal under the Civil Rights Act for a company over 15 employees to discriminate when hiring based on race, creed, color or national origin. There is no exemption for white women.
Courts have said however, that the Civil Rights Act does allow companies to voluntarily adopt an affirmative action program designed to correct historical discrimination in hiring. Those programs have to be narrowly tailored in time and scope so that it only remedies past discrimination.
The Getty Foundation seems to have been created with this internship with this limitation in mind:
Be of a group underrepresented in museums and visual arts organizations, including, but not limited to, individuals of African American, Asian, Latino/Hispanic, Native American, or Pacific Islander descent
Of course, if there is no historical discrimination of say, Asians, in museums or visual arts organizations or they are well represented now, then it is totally illegal to bias your hiring towards them.
Plus, even if you have an affirmative action program, I’m pretty sure you’re not allowed to put a racial preference on your job application requirements.
That standard is why companies don’t usually implement affirmative action programs unless ordered by the court to do so. It requires effectively measuring the protected class’ participation in a particular business or trade and demonstrating a history of discrimination that needs to be correcting.
It is actually illegal to discriminate or retaliate against someone who participated in an employment discrimination investigation or lawsuit - for obvious reasons.