How to get all post categories without custom post type categories?

As pointed out by Tom, this could end up being an expensive query, though from my anecdotal evidence from trying this on a rather large database (granted, only a handful of post types), I think you could write a decently sufficient query.

If you’re using caching to store the categories, that could also alleviate some of the potential performance issues.

Here’s the query I used for testing (but with my own post types):

SELECT DISTINCT
    tt.taxonomy
FROM
    wp_term_taxonomy tt
JOIN
    wp_term_relationships tr ON( tr.term_taxonomy_id = tt.term_taxonomy_id )
WHERE
    tr.object_id IN ( SELECT ID FROM wp_posts WHERE post_type IN ( 'list', 'of', 'normal', 'post', 'types' ) );

Converting this to something more portable for WordPress:

<?php
global $wpdb;

$post_types   = [ 'list', 'of', 'normal', 'post', 'types' ];
$placeholders = array_fill( 0, count( $post_types ), '%s' );

$sql = <<<SQL
SELECT
    tt.taxonomy
FROM
    {$wpdb->term_taxonomy} tt
JOIN
    {$wpdb->term_relationships} tr ON( tr.term_taxonomy_id = tt.term_taxonomy_id )
WHERE
    tr.object_id IN ( SELECT ID FROM {$wpdb->posts} WHERE post_type IN ( {$placeholders} ) );
SQL;

$query   = $wpdb->prepare( $sql, $post_types );
$results = $wpdb->get_col( $query );

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