Advanced Custom Fields, WordPress, Javascript Tabbed Content

There are some issues with your js file. Try this:

jQuery(document).ready(function($) {
  $(".tabs li").each(function() {
    $(this).on("click", function() {
      var tab_id = $(this).attr('data-tab');

      $('.tabs .tab-link.current').removeClass('current');
      $('.tab-content.current').removeClass('current');

      $(this).addClass('current');
      $("#" + tab_id).addClass('current');
    });
  });
});

You can see this jsfiddle for demo.