[Vuejs]-Vue.js – how to update childs data on parent's data update without this.$parent[…]

You should have status itself become a computed property.

Remove it from data declaration and do:

computed: {
 status() { return this.$parent[this.type] == undefined ? true : this.$parent[this.type]; }
}

You can use it like:

:class="{isNotVisible : !status}"

JSFiddle here.