There are at least three ways to answer this question.
First, we can argue that racial prejudice and discrimination have helped white people. From before the independence of the United States until the 1960s, it was legal to discriminate against members of racial minorities. Liberals generally argue that whites benefited from this because they received the benefits of (mostly black) manual labor and because they did not have to compete with minorities for jobs above a certain menial level. From this point of view, racial prejudice and discrimination helped whites and allowed them to build and consolidate their status as the dominant race in the United States. Even though racial discrimination is no longer legal, the impact of past discrimination and of current prejudice (we can argue) continues to help whites today.
Second, we can argue that racial discrimination today hurts white people. This is the argument behind much of the opposition to affirmative action programs. Since the early 1970s, various governmental and other organizations have had policies that in some ways have given preference to non-whites. Conservatives argue that these policies have unfairly harmed white Americans.
Finally, we can look at this question from a moral point of view. Martin Luther King, Jr. once said that injustice anywhere was a danger to justice everywhere. We can argue that whites have been harmed by racism because it makes the country in which they live less just. Whites who are not racist are harmed by having to live in such a country. Whites who are racist are harmed psychologically and spiritually by their attitudes.
Thus, there are many different ways in which to look at this question.