JSFiddle - React, Tailwind, and code Playground

HTML

<ul id="whatson">
  <li>
     <span class="chkdate">06/01</span> 
     somestuff1
  </li> 
  <li>
     <span class="chkdate">06/04</span> 
     somestuff1
  </li> 
  <li>
     <span class="chkdate">06/05</span> 
     somestuff2
  </li>
</ul>

JavaScript

var today = new Date();
$("#whatson .chkdate").each(function() {
    var datepieces = $(this).text().split("/");
    var month = datepieces[0];
    var day = datepieces[1];
    
    if (month < (today.getMonth() + 1))
        $(this).closest("li").hide();
    
    if (day < today.getDate())
        $(this).closest("li").hide();
});