How to make custom post taxonomy looks like regular categories?

Within your functions.php:

function custom_admin_scripts( $hook ) {

    if ( $hook == 'post.php' && get_post_type() == 'your_custom_post_type_key' ) {
        wp_enqueue_style( 'your_custom_post_type_key', get_stylesheet_directory_uri() . '/my_css_file.css', array(), false, 'all' );
    }

}

add_action( 'admin_enqueue_scripts', 'custom_admin_scripts' );

Change your_custom_post_type_key to your custom post type key
Change /my_css_file.css to your real path towards your css file.

Within your css file:

#{your_custom_taxonomy_key}-adder {
    display: none !important;
}

Change {your_custom_taxonomy_key} to your custom taxonomy key.

That CSS selector will hide, as aksed, the whole adder section.

This should do it.