Remove taxonomy menu without removing the metabox?

I think the simple answer based on my testing locally is to change the value from true to false in this line of code which is included when you register taxonomy support for custom post types.

'show_ui' => false,

Here’s the full code i used:

add_action( 'init', 'executive_type_taxonomy' );
function executive_type_taxonomy() {

register_taxonomy( 'portfolio-type', 'portfolio',
    array(
        'labels' => array(
            'name'          => _x( 'Types', 'taxonomy general name', 'executive' ),
            'add_new_item'  => __( 'Add New Portfolio Type', 'executive' ),
            'new_item_name' => __( 'New Portfolio Type', 'executive' ),
        ),
        'exclude_from_search' => true,
        'has_archive'         => true,
        'hierarchical'        => true,
        'rewrite'             => array( 'slug' => 'portfolio-type', 'with_front' => false ),
        'show_ui'             => false,
        'show_tagcloud'       => false,
    )
);

}

You could also remove the admin menu based on user roles and capabilities.