Actions have consequences. In this case, washing one’s robes (in the blood of the Lamb) provides access to delightful blessings. The inclusion of the words so that
lays emphasis on obligation. That obligation is underscored by the implication that those who do not wash their robes have no right to the tree of life and cannot enter the city.
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.