Holiness is not cutting ourselves off from this sinful world. It means to separate ourselves from their sinful works. We are to live in this world with the purpose of reaching out to the unsaved. See Jude 22,23 for details.
Nehemiah 10:28 Now the rest of the people—the priests, the Levites, the gatekeepers, the singers, the Nethinim, and all those who had separated themselves from the peoples of the lands to the Law of God, their wives, their sons, and their daughters, everyone who had knowledge and understanding—