[Vuejs]-Local storage data not being bound to data

beforeMount is a lifecycle hook, not a method. It must be defined directly within options, not inside methods:

export default {
  name: "FooterComponent",
  data() {
    return {
      privacy_modal: false,
      privacy_title: '',
      privacy_content: ''
    };
  },

  beforeMount() {
    this.privacy_title = localStorage.getItem("privacy_title"); // || "some default value"
  },

  methods: {
    // custom methods
  }
};

Also, don’t forget to update local storage, as demanded by your app logic.