The classical liberal strand in Western political philosophy has historically opposed special government privileges for groups and prized equality before the law. Classical liberals favored eliminating the benefit of clergy and the privileges of the nobility. They fought against slavery. And, unlike some progressives of the late nineteenth and early twentieth century, they opposed Jim Crow.
Whether classical liberalism should embrace laws that prevent private actors from treating people unequally on the basis of characteristics, like race and sex, is a more complicated question. But in my view, given the long history of Jim Crow in the United States, laws against discrimination on the basis of race or ethnicity were justified to break ingrained habits encouraged by government discrimination against African-Americans. But here again the classical liberal view molded these laws into general prohibitions against discrimination, not special privileges for certain groups.
In the 1960s and 1970s progressives began to transform these laws into mechanisms of social engineering that took account of race in their planning. But for a brief period in Reagan administration, the classical liberal strand of universalism reasserted itself as part of the core ideology of the Republican party. The result was an effort to treat laws on discrimination as general prohibitions on discrimination on the basis of race and ethnicity, no matter which race and ethnicity was at issue. Colorblindness was banner under which the movement marched.
Sadly, this movement has dissipated.