Nihilistic Politics?

A probably unoriginal thought:

Since Nietzsche (or perhaps since the Sophists?), there has been a tradition in Western culture that denies there is any such thing as objective reality. Curiously, some of the members of this tradition are also members of a political progressive stream which stringently objects to oppression and injustice against vulnerable classes. But this occurred to me: if there is no such thing as reality, there is no such thing as oppression and injustice. Nihilism undermines a politics of justice.