Relativism does not imply that all truth-claims, moral positions, ways of experiencing reality, etc. are “equally valid”. Such a claim actually invokes some absolute notion of validity.
Consider, by way of analogy, the relativity of space as understood by modern physicists. Abolishing the idea of absolute position in space does not mean that “all objects are equally far away from the centre of the universe”. It means that the universe has no centre — or, better yet, that the idea of “the centre of the universe” has no meaning. We can only measure the position of any object in relation to the position of other objects
Relativism does not imply that it is wrong to make moral judgments of actions committed by members of cultured different from our own. Again, such a claim requires some absolute standard of moral right which makes such judgments wrong.
Relativism does not imply that we cannot make judgments of right and wrong, true and false, etc. It only denies belief in any absolute basis for such judgments.
In other words, relativism does not prevent us from making assertions; it only changes how we understand “what it is that we are doing” when we make assertions.
Even this small change has extensive and, I think, very fruitful implications.