How do I exclude a custom taxonomy from the post loop

You would want to use the NOT EXISTS operator along with passing the taxonomy slug, which tells the query not to include any of a chosen category from your custom taxonomy inside the loop.

To exclude all posts that are in the taxonomy “fruit” (regardless of fruit kind), here is the snippet:

$args = array(
    'post_type'      => 'post',
    'tax_query'      => array(
        array(
            'taxonomy' => 'fruit',
            'operator' => 'NOT EXISTS'
        )
    )
);

$query = new WP_Query( $args );