Metadata navigation is not visible to users with read permissions
This is a common issue when you start using the metadata navigation in your SharePoint 2013 site, let’s check how easily you can make it available to all the users.
By default, when you create a term in the navigation term set, SharePoint selects Term-Driven Page with Friendly URL, if you leave this option selected the term will be visible only to the users with write permissions.
To fix this issue you just need to select Simple Link or Header and provide the url to the desired page.
To get access to both options you need to select the Navigation tab.
Simple Link or Header it’s more robust than Term-Driven Page with Friendly URL, it allows you to make the navigation visible to all the users and it also let you add external URLs to the navigation.