Getting rid of menu items on a custom taxonomy

This is not your code I suspect, as there are really many errors in your code. I’m going to list them

Firstly, you are registering your custom post type inside a function that you hook to init, which is fine. Then you register your taxonomies outside that function. What the reason bhin that is, I don’t know. You should register both your taxonomies and custom post type inside your function, as your taxonomies are registered to your custom post type

Secondly, register_taxonomy( $taxonomy, $object_type, $args ); looks like this. The $object_type parameter, although taking an array or a string can just be a string, as you are only registering your taxonomy to one custom post type

Thirdly, in the event_cat taxonomy, this line 'labels' => array( is missing, breaking everything

Fourthly, in the event_tag taxonomy, there is this piece this */ of nothingness, which also breaks your code

Lastly, if this was your code, you should have not registered category and tags. Here is the code that registered categories and tags

register_taxonomy_for_object_type('category', 'event_type');
register_taxonomy_for_object_type('post_tag', 'event_type');

So, after all of this, your code should be

function event_post_example() {

register_post_type( 'event_type',
    array(
    'labels' => array(
        'name' => __('Events Posts', 'baretheme'),
        'singular_name' => __('Event Post', 'baretheme'),
        'all_items' => __('All Event Posts', 'baretheme'),
        'add_new' => __('Add New Event Post', 'baretheme'),
        'add_new_item' => __('Add New Event Type', 'baretheme'),
        'edit' => __( 'Edit', 'baretheme' ),
        'edit_item' => __('Edit Post Types', 'baretheme'),
        'new_item' => __('New Post Type', 'baretheme'),
        'view_item' => __('View Post Type', 'baretheme'),
        'search_items' => __('Search Post Type', 'baretheme'),
        'not_found' =>  __('Nothing found in the Database.', 'baretheme'),
        'not_found_in_trash' => __('Nothing found in Trash', 'baretheme'),
        'parent_item_colon' => ''
    ), /* end of arrays */
    'description' => __( 'This is the example event post type', 'baretheme' ), /* Custom Type Description */
    'public' => true,
    'publicly_queryable' => true,
    'exclude_from_search' => false,
    'show_ui' => true,
    'query_var' => true,
    'menu_position' => 9,
    'menu_icon' => get_stylesheet_directory_uri() . '/library/images/custom-post-icon.png',
    'rewrite'   => array( 'slug' => 'event_type', 'with_front' => false ),
    'has_archive' => 'event_type',
    'capability_type' => 'post',
    'hierarchical' => false,

    'supports' => array( 'title', 'editor', 'author', 'thumbnail', 'excerpt', 'trackbacks', 'custom-fields', 'comments', 'revisions', 'sticky')
    ) /* end of options */
); /* end of register post type */

register_taxonomy( 'event_cat','event_type',
    array(
        'labels' => array(
        'name' => __( 'Event Categories', 'baretheme' ),
        'singular_name' => __( 'Event Category', 'baretheme' ),
        'search_items' =>  __( 'Search Event Categories', 'baretheme' ),
        'all_items' => __( 'All Event Categories', 'baretheme' ),
        'parent_item' => __( 'Parent Event Category', 'baretheme' ),
        'parent_item_colon' => __( 'Parent Event Category:', 'baretheme' ),
        'edit_item' => __( 'Edit Event Category', 'baretheme' ),
        'update_item' => __( 'Update Event Category', 'baretheme' ),
        'add_new_item' => __( 'Add New Event Category', 'baretheme' ),
        'new_item_name' => __( 'New Event Category Name', 'baretheme' )
    ),
    'hierarchical' => true,
    'show_admin_column' => true,
    'show_ui' => true,
    'query_var' => true,
    'rewrite' => array( 'slug' => 'event-slug' ),
    )
);

register_taxonomy( 'event_tag','event_type',
    array(
        'labels' => array(
        'name' => __( 'Event Tags', 'baretheme' ),
        'singular_name' => __( 'Event Tag', 'baretheme' ),
        'search_items' =>  __( 'Search Event Tags', 'baretheme' ),
        'all_items' => __( 'All Event Tags', 'baretheme' ),
        'parent_item' => __( 'Parent Event Tag', 'baretheme' ),
        'parent_item_colon' => __( 'Parent Event Tag:', 'baretheme' ),
        'edit_item' => __( 'Edit Event Tag', 'baretheme' ),
        'update_item' => __( 'Update Event Tag', 'baretheme' ),
        'add_new_item' => __( 'Add New Event Tag', 'baretheme' ),
        'new_item_name' => __( 'New Event Tag Name', 'baretheme' )
    ),
    'hierarchical' => false,
    'show_admin_column' => true,
    'show_ui' => true,
    'query_var' => true,
    )
);
}

add_action( 'init', 'event_post_example');