Remove Post Categories & Tags

functions.php

add_action( 'init', 'post_cat_taxonomy_cleanup', 11 );
function post_cat_taxonomy_cleanup() {
	global $wp_taxonomies;
	$wp_taxonomies['category']->object_type = array_diff( $wp_taxonomies['category']->object_type, array( 'post' ) );
}

add_action( 'init', 'post_tag_taxonomy_cleanup', 11 );
function post_tag_taxonomy_cleanup() {
	global $wp_taxonomies;
	$wp_taxonomies['post_tag']->object_type = array_diff( $wp_taxonomies['post_tag']->object_type, array( 'post' ) );
}