You haven't included
get_footer() in your template. They will load header.php and footer.php which should include
wp_footer(). Those last two functions are important because that's where scripts are loaded.
If your shortcode depends on a script being loaded in the header or the footer, then you need
wp_footer(), thats where plugins load their scripts. Looking at the code for this plugin (tell me if that's not it), then the script for it loads in
So at the very least your template needs to look like this:
Template Name: Social Login Page
<?php wp_head(); ?>
<?php echo do_shortcode('[wordpress_social_login]'); ?>
Looking at the plugin code, the only way it could've worked on your localhost is is you had not turned on the "popup" functionality, which requires the script.
Also, even if you're not using
wp_head(), you still need the
<body> tags to be valid HTML.