wp_dequeue_style and wp_dequeue_script not working on server but does work on local xampp

If you want to dequeue scripts & styles for a specific page based on the slug of the page. You can get the slug in various ways and use it instead of $_SERVER['REQUEST_URI'].

Use if( is_page( array( 'my_page') instead of if(basename($_SERVER['REQUEST_URI'])=='my_page')

function wpse_289574_dequeue_scrips() {
   if(is_page( array( 'my_page')){
       wp_dequeue_style( 'taxonomy-image-plugin-public' );
       ...       
   }
}

How to get the slug of a page:

$qo = $GLOBALS['wp_the_query']->get_queried_object();
$cp = sanitize_post($qo);
$slug = $cp->post_name;

Taken from: How to retrieve the slug of current page?

function wpse_289574_dequeue_scrips() {
   if($slug =='my_page'){
       wp_dequeue_style( 'taxonomy-image-plugin-public' );
       ...       
   }
}

Current hook to dequeue is wp_enqueue_scripts.