JSFiddle - React, Tailwind, and code Playground

HTML

<script src="//code.jquery.com/jquery-3.3.1.slim.min.js"></script>
<link rel="stylesheet" href="//stackpath.bootstrapcdn.com/bootstrap/4.1.0/css/bootstrap.min.css">
<script src="//cdnjs.cloudflare.com/ajax/libs/popper.js/1.14.0/umd/popper.min.js"></script>
<script src="//stackpath.bootstrapcdn.com/bootstrap/4.1.0/js/bootstrap.min.js"></script>
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css">
<div class="text-center row">
  <ul  class="col-md-12 secondNav">
    <li class="navbar-brand nav-item" style="margin-right: 9%">
      <a href="#" ><strong>INICIO</strong> </a>
    </li>
    <li  class="navbar-brand nav-item" >
      <a href="#"><strong>COMPARAR</strong></a>
    </li>
  </ul>
</div>

CSS

.alt-background {
  background-color: lightgray;
}

JavaScript

const listItems = document.querySelectorAll('.navbar-brand');

listItems.forEach(li => {
	li.addEventListener('click', () => {
		li.classList.toggle('alt-background');
  })
})