Remove WordPress Customizer links from the Admin Toolbar and dashboard by changing the body class back to 'no-customize-support'. This is a way to show only the original admin toolbar links for themes that don't support the Customizer.

wp-hide-customizer-admin-links

/**
 * Remove customizer links from the Admin Toolbar and dashboard by changing the body class back to 'no-customize-support'
 */
function pmc_remove_customize_support() {
	// Copied from wp_customize_support_script() in wp-includes/theme.php
	?>
	<script type="text/javascript">
		(function() {
			var b = document.body, c = 'className', cs = 'customize-support', rcs = new RegExp('(^|\\s+)(no-)?'+cs+'(\\s+|$)');
			b[c] = b[c].replace( rcs, ' ' );
			b[c] += 'no-customize-support';
		}());
	</script>
	<?php
}
add_action( 'wp_before_admin_bar_render', 'pmc_remove_customize_support', 20 );