Here, sanctify does not mean "consecrate" or "purify." Remember that they were already cleaned up by this time. In this context, it means "set apart." The priests were to separate themselves or get away.
Deuteronomy 5:4-5 further expounds on this. The people's rejection was at least partly based on their own accurate recognition of their sinfulness. Despite the fact that they were cleaned up, their recognition of their sinfulness—when confronted with God's holiness, which was demonstrated by the mountain quaking, lightning cracking huge peals of thunder, and the trumpet blaring—was why God accepted their proposal immediately. "Stop them from coming any closer," He told Moses. Therefore, their refusal to draw near to God was based on a correct assessment of their unacceptability to do the job of a priest—despite the fact that they had cleansed themselves and their clothing, externally.
