It still should be okay, maybe there is a delay on the window load and a timeout could actually fix it:
jQuery(function($){
const load = () => {
$('.asp_label').on('click', function(){
$(this).parent().find('.asp_label').removeClass('asp_label_selected');
$(this).addClass('asp_label_selected');
});
}
load();
setTimeout(()=>load(), 1500);
});