Liberal Democracy and Multiculturalism

How are the two mutually exclusive? If one begins from the premise that we are all equal, how does multiculturalism mean the upholding of bigoted and racist beliefs of one culture above all others? How is multiculturalism not the work of constructing the possibility for multiple strata of cultures to work together on an equal standing of inclusiveness? Isn't a qualitative evaluation favoring one culture over another oppressive, and, regardless of intentions, isn't disregarding the fluidity of different strata of cultural identity typical of immigration, even generational, an inaccuracy?