It seems that the WebViewClient methods such as shouldInterceptRequest(), onPageStarted(), and shouldOverrideUrlLoading() only listen for URL changes that cause the WebView to load a new page. Is there a way to detect URL changes for fragment IDs, i.e. index.html#fragment_id, on a WebView?
As mitvenkatesan described in his comment to the question, this can be achieved by overriding the window.onhashchange() event of the page inside the WebView.
It turns out that this solution has already been addressed in another question.