JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://code.jquery.com/jquery-3.1.1.min.js" integrity="sha256-hVVnYaiADRTO2PzUGmuLJr8BLUSjGIZsDYGmIJLv2b8=" crossorigin="anonymous"></script>

<h2>
This "custom" dropdown doesn't resize correctly.
</h2>
<div class="dropdown">
  <select id="real_dropdown">
    <option disabled="">Options</option>
    <option value="long">Something super long in here</option>
    <option value="short">Short</option>
  </select>
</div>
<select id="width_tmp_select">
  <option id="width_tmp_option"></option>
</select>

CSS

.dropdown {
  width: 280px;
  overflow: hidden;
  background: url(https://secure.echobox.com/img/dropdown_arrow.png) no-repeat right transparent;
  border: 1px solid black;
  white-space: nowrap;
  background-size: 18px 5px;
}

.dropdown select {
  width: 100%;
  background: transparent;
  font-size: 16px;
  border: 0;
  border-radius: 0;
  -webkit-appearance: none;
  -moz-appearance: none;
  font-family: "proxima-nova", Helvetica, Arial, sans-serif;
  white-space: nowrap;
  color: #56646E;
}

#width_tmp_select{
  display : none;
}

JavaScript

$(document).ready(function() {
  $('.dropdown').change(function(){
    $("#width_tmp_option").html($('.dropdown option:selected').text()); 
    $(this).width($("#width_tmp_select").width()+30);  
  });
});