JSFiddle - React, Tailwind, and code Playground

HTML

<div class="field__group">
  <div class="ranged">
    <div class="field field__left">
      <label for="birth_month" class="form-label">Your Birth Month</label>
      <select id="birth_month" name="birth_month" style="background: blue;">
        <option value="1">January</option>
        <option value="2">February</option>
        <option value="3">March</option>
        <option value="4">April</option>
        <option value="5">May</option>
        <option value="6">June</option>
        <option value="7">July</option>
        <option value="8">August</option>
        <option value="9">September</option>
        <option value="10">October</option>
        <option value="11">November</option>
        <option value="12">December</option>
      </select>
    </div>
    <span class="range"></span>
    <div class="field field__right">
      <label for="birth_day">Your Birth Day</label>
      <select id="birth_day" name="birth_day">
        <option value="1">1</option>
        <option value="2">2</option>
        <option value="3">3</option>
        <option value="4">4</option>
        <option value="5">5</option>
        <option value="6">6</option>
        <option value="7">7</option>
        <option value="8">8</option>
        <option value="9">9</option>
        <option value="10">10</option>
        <option value="11">11</option>
        <option value="12">12</option>
        <option value="13">13</option>
        <option value="14">14</option>
        <option value="15">15</option>
        <option value="16">16</option>
        <option value="17">17</option>
        <option value="18">18</option>
        <option value="19">19</option>
        <option value="20">20</option>
        <option value="21">21</option>
        <option value="22">22</option>
        <option value="23">23</option>
        <option value="24">24</option>
        <option value="25">25</option>
        <option value="26">26</option>
        <option value="27">27</option>
        <option...

CSS

option.hidden {
  display: none;
}

JavaScript

$('document').ready(function($) {
  $('#birth_month').change(function(e) {
    //   e.preventDefault();
    $('#birth_day option').show();

    switch ($('#birth_month').val()) {

      case '2':
        $('#birth_day option[value="30"]').hide();
        //      $('#birth_day option[value="31"]').hide();
        //      break;
      case '2':  /* or use the 2 lines above */
      case '4':
      case '6':
      case '9':
      case '11':
        $('#birth_day option[value="31"]').hide();
     //   break;
        //     default:
        //       $('#birth_day option').show();
        //       break;
    }
  });
});