Ajax call returning 0

When defining an Ajax handler, you should consider defining both for logged in and non logged in users. You can do so by using:

add_action('wp_ajax_my_handler', 'callback_function');
add_action('wp_ajax_nopriv_my_handler', 'callback_function');

Now, as for your question. We can turn this code into a REST endpoint, if you are interested, which is faster and easier to set up. Let’s start by defining a route.

add_action( 'rest_api_init', function () {
    register_rest_route( 'karts', '/ins_get_membershiptypes_from_country/', array(
            'methods' => 'GET',
            'callback' => 'ins_get_membershiptypes_from_country_callback'
    ) );
});

At this point, we can run our quest by accessing:

www.example.com/wp-json/karts/ins_get_membershiptypes_from_country/

Now the Ajax call. Use this to localize your script, and pass the site URL:

wp_localize_script( 'member-front-script','ins_membership_ajax', array(
    'ajax_url' => site_url()
));

So, we can access the path in our Ajax call:

   $("#member_country").change(function() {
        var country = $(this).val();
        alert(country);
        var ajax_url_mtypes = ins_membership_ajax.ajax_url + '/kartsins_get_membershiptypes_from_country';
        alert(ajax_url_mtypes);
        jQuery.ajax({
        url:ajax_url_mtypes,            
        method:'GET',
        data : { country : country},
        dataType: 'json',
        success:function(response) {
          //var resp = $.trim(response);
          alert(response);
          //$("#ins-member-profile-select-state").html(resp);
      }
      });

Not that I have defined a JSON data type for the call. This way, you will get a Json response by default.