How to allow user to select empty string on Select2

You can set the allowClear option to true.

$("#e6").select2({
    allowClear: true,
    placeholder: "Search for a movie",
    ...

When set to true, the allowClear option causes the Select2 control to display a clear button, but you must also specify the placeholder option for it to work.

Here’s a jsfiddle showing it work for a Select2 that uses ajax.