Remount when navigating to the same component but different routes

[melang982]

I have two routes that both should display Home component:

<Route path="/tags/:id" component={Home} />
<Route path="/" component={Home} />

When user is at URL /tags/cats and clicks on a different tag, for ex. /tags/dogs, no remount happens, and that's indeed the intended behavior.
But if the user is at the homepage / and clicks on a tag and vice-versa, the component remounts. How can I avoid this remounting?