Add a button in GitHub UI to ignore whitespace in diffs. To install in a browser with a UserScript extension (e.g., Tampermonkey), click the "Raw" button.

github_whitespace_button.user.js

// ==UserScript==
// @name           Ignore whitespace button on GitHub
// @description    Adds a button in GitHub UI to ignore whitespace changes in commits
// @author         lsloan
// @namespace      https://gist.github.com/lsloan/e51ac64706b86cc1942616004f2be3bd
// @updateURL      https://gist.github.com/lsloan/e51ac64706b86cc1942616004f2be3bd/raw/github_whitespace_button.user.js
// @match          https://github.com/*
// @version        1.5
// @run-at         document-end
// @grant          none
// ==/UserScript==

function AddWhitespaceButton()
{
	var hasWhitespaceSwitch = window.location.search.match( /[\?&]w=/ ) !== null;
	
	AddButtonInPullRequestReview( hasWhitespaceSwitch );
	AddButtonInCommits( hasWhitespaceSwitch );
}

function AddButtonInPullRequestReview( hasWhitespaceSwitch )
{
	var toc = document.querySelector( '.pr-toolbar .dropdown-menu' );
	
	if( !toc || document.getElementById( 'js-lsloan-whitespace-button' ) )
	{
		return;
	}
	
	var button = CreateButton( hasWhitespaceSwitch );
	button.className = 'dropdown-item' + ( hasWhitespaceSwitch ? ' selected' : '' );
	
	if( hasWhitespaceSwitch )
	{
		var checkmark = document.createElement( 'b' );
		checkmark.className = 'octicon';
		checkmark.textContent = '✓';
		button.appendChild( checkmark );
	}
	
	toc.appendChild( button );
}

function AddButtonInCommits( hasWhitespaceSwitch )
{
	var toc = document.querySelector( '#toc > .btn-group.right' );
	
	if( !toc || document.getElementById( 'js-lsloan-whitespace-button' ) )
	{
		return;
	}
	
	var button = CreateButton( hasWhitespaceSwitch );
	button.className = 'btn btn-sm right' + ( hasWhitespaceSwitch ? ' selected' : '' );
	button.style.marginRight = '10px';
	
	//$( document ).pjax( button, '#js-repo-pjax-container' );
	
	toc.parentNode.insertBefore( button, toc.nextSibling );
	
	var pr = $( '.js-pull-request-tab' );
	
	if( pr && !pr.RegisteredWhitespaceClick )
	{
		pr.RegisteredWhitespaceClick = true;
		
		$( document ).on( 'click', pr, function( e )
		{
			setTimeout( function()
			{
				button.href = UpdateQueryString( 'w', hasWhitespaceSwitch ? null : '1' );
			}, 0 );
		} );
	}
}

function CreateButton( hasWhitespaceSwitch )
{
	var button = document.createElement( 'a' ); 
	button.id = 'js-lsloan-whitespace-button';
	button.textContent = 'Ignore whitespace';
	button.href = UpdateQueryString( 'w', hasWhitespaceSwitch ? null : '1' );
	
	return button;
}

AddWhitespaceButton();

$( document ).on( 'pjax:complete', AddWhitespaceButton );

// http://stackoverflow.com/a/11654596/2200891
function UpdateQueryString(key, value)
{
	var re = new RegExp("([?&])" + key + "=.*?(&|#|$)(.*)", "gi"),
		url = window.location.href,
		hash;
	
	if (re.test(url))
	{
		if (typeof value !== 'undefined' && value !== null)
		{
			url = url.replace(re, '$1' + key + "=" + value + '$2$3');
		}
		else
		{
			hash = url.split('#');
			url = hash[0].replace(re, '$1$3').replace(/(&|\?)$/, '');
			
			if (typeof hash[1] !== 'undefined' && hash[1] !== null)
			{
				url += '#' + hash[1];
			}
		}
	}
	else if (typeof value !== 'undefined' && value !== null)
	{
		var separator = url.indexOf('?') !== -1 ? '&' : '?';
		hash = url.split('#');
		url = hash[0] + separator + key + '=' + value;
		
		if (typeof hash[1] !== 'undefined' && hash[1] !== null) 
		{
			url += '#' + hash[1];
		}
	}
	
	return url;
}

Issues:

1. When the page refreshes with "w=1" URL, "Ignore whitespace" no longer appears in the list of options. However, manually reloading the page with that URL, "Ignore whitespace" does appear, along with a check mark to show it's active.
2. GitHub bug: When ignore whitespace mode is enabled, the "line notes" feature stops working. That makes it difficult (impossible?) to give code review feedback.