The phrase wash their robes
refers to people dirty with sin (filthy
in Revelation 22:11) seeking forgiveness in the blood of the Lamb (Revelation 7:14). Note the active voice here; these people do the washing themselves. Note too the present tense; this washing is repeated as sin and filth remain realities. The active voice is fully in line with the closing words of Revelation 22:12, where Christ distributes recompense to each for what he has done.
The emphasis lies on the personal obligation to respond properly to the gospel of the exalted Lamb.
14 Blessed are those who wash their robes, so that they may have the right to the tree of life and that they may enter the city by the gates.