Fasani posted a solution on the repository's issue page at GitHub:
substitute the whole $newSelect.on("blur", function() { ... } function by
$newSelect.on("blur", function() {
  var that = this;
  $(this).find(' ~ .dropdown-content span').off('click');
  $(this).find(' ~ .dropdown-content span').on('click', function() {
    $(that).trigger('close');
  });
  var containers = $(".select-dropdown");
  if (!multiple && !containers.is(e.target)) {
    $(this).trigger("close");
  }
  options.find("li.selected").removeClass("selected");
});
Unfortunatly, this solution have a downside in which the dropdown only closes if an option is selected (not if the person clicks out of the dropdown list). Personally, I guess it's worth it.
If you want to limit this "downside" to IE only, you could put a conditional like the following (based on this stackoverflow page):
var isIE = function() {
    var msie = window.document.documentMode;
    if (msie <= 11) return true;
    else return false;
}
$newSelect.on('blur', function() {
    if (isIE()){
        var that = this;
        $(this).find(' ~ .dropdown-content span').off('click');
        $(this).find(' ~ .dropdown-content span').on('click', function() {
            $(that).trigger('close');
        });
        var containers = $(".select-dropdown");
        if (!multiple && !containers.is(e.target)) {
            $(this).trigger("close");
        }
    } else {
        if (!multiple) {
            $(this).trigger('close');
        }
    }
    options.find('li.selected').removeClass('selected');
});