JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://code.jquery.com/jquery-1.12.4.min.js"></script>
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.min.js"></script>
<link rel="stylesheet" href="https://code.jquery.com/ui/1.12.0/themes/smoothness/jquery-ui.css">
<table>
<tbody>
  <tr>
    <th>From:</th>
    <td><input id="start" type="text"/></td>
  </tr>
  <tr>
    <th>To:</th>
    <td><input id="end" type="text"/></td>
  </tr>
</tbody>
</table>

CSS

body {
  font-family: cursive;
}

.ui-datepicker-calendar { display: none; }

JavaScript

$("#start").datepicker({
  changeMonth : true,
  changeYear : true,
  dateFormat : "MM yy",
  minDate : new Date(2017, 0, 1),
  yearRange : "1970:+1",
  showButtonPanel : true,
  onClose: function() {
    var month = $("#ui-datepicker-div .ui-datepicker-month :selected").val();
    var year = $("#ui-datepicker-div .ui-datepicker-year :selected").val();

    var selected = new Date(year, month, 1);

    $(this).datepicker('setDate', selected);

    var date = new Date(year, month, 1);
    date.setMonth(selected.getMonth() + 11);

    $("#end").datepicker("option", "maxDate", date);
    $("#end").datepicker("option", "minDate", selected);
  }
});

$("#end").datepicker({
  changeMonth : true,
  changeYear : true,
  dateFormat : "MM yy",
  minDate : new Date(2017, 0, 1),
  yearRange : "1970:+1",
  showButtonPanel : true,
  onClose: function() {
    var month = $("#ui-datepicker-div .ui-datepicker-month :selected").val();
    var year = $("#ui-datepicker-div .ui-datepicker-year :selected").val();

    var selected = new Date(year, month, 1);

    $(this).datepicker('setDate', selected);

    var date = new Date(year, month, 1);
    date.setMonth(selected.getMonth() + 11);

    $("#start").datepicker("option", "maxDate", selected);
    $("#start").datepicker("option", "minDate", date);
  }
});