This statement is true in a number of ways. First, to look at "Progressives" as a group is to acknowledge that they represented a fairly broad swath of reform-minded Americans, united primarily by their commitment to reform. On the one hand, many advocates of racial equality, like William Monroe Trotter, Ida B. Wells, and W. E. B. DuBois, were very much included in the Progressive ranks. They advocated anti-lynching laws and other measures to promote African American rights. On the other hand, many Progressives, especially Southern political leaders, were committed racists.
President Woodrow Wilson infamously made a point of desegregating federal jobs very soon after taking his place in the White House. Southern governors like Charles Aycock of North Carolina avidly promoted public spending on education as well as other Progressive measures, like restraining the trusts. But they also did much to promote Jim Crow laws and institutional discrimination in their states.
Another reason this can be said of Progressives is because many of their reform efforts were tinged by racism, xenophobia, or, at best, condescending views about other cultures. Eugenics, a cause taken up by some Progressives, was seen as a means of creating a better future through genetic manipulation (i.e., by keeping people with supposedly "bad genes" from reproducing). These measures disproportionately targeted people of color and played on contemporary views of racial hierarchies. The enthusiasm that many Progressives had for many other reforms was rooted in xenophobia and the assumption that middle-class white culture was normative. The temperance movement in particular held that supposedly hard-drinking immigrants could reform their lives through turning away from alcohol. Over time, some urban reformers like Jane Addams turned away from these assumptions, but even she began her career with less than favorable views of the people she worked with.
One of the central political figures of the period, Theodore Roosevelt, embodied some of these apparent paradoxes. On the one hand, Roosevelt was the consummate reformer. His "New Nationalism" platform of 1912 contained reforms that would be considered radical in today's political climate. But Roosevelt held, as many of his day did, a belief in Anglo-Saxon superiority. It lay at the root of his commitment to the "strenuous life," and it strongly informed his foreign policy positions. All in all, the Progressives were men and women of their time, even if some of the reform initiatives they pursued were strikingly modern. And their time, the early twentieth century, was witness to a virulent form of racism and open efforts to maintain white supremacy.