[Vuejs]-Vuejs Hide/Show Elements refreshes when Routes change

you can use vuex for solved this problem.
https://vuex.vuejs.org/

Vuex is a state management pattern + library for Vue.js applications. It serves as a centralized store for all the components in an application, with rules ensuring that the state can only be mutated in a predictable fashion. It also integrates with Vue’s official devtools extension (opens new window)to provide advanced features such as zero-config time-travel debugging and state snapshot export / import.