Bootstrap 4 подтверждает, что проверка пароля не работает

Вам нужно добавить одну строку кода в открывающий тег формы.

<form class = "form-signin needs-validation" novalidate oninput='confirmPassword.setCustomValidity(confirmPassword.value != newPassword.value ? true : false)'>

Я сделал codepen. Пожалуйста, проверьте это.

https://codepen.io/subhojitghosh/pen/JjROMLO

Ссылка: https://stackoverflow.com/a/53065577/10850734

Я упростил вашу логику проверки и использовал атрибуты disabled и hidden HTML. Вы можете увидеть работающий отрефакторенный код здесь, в codeandbox

JS-код:

// To ensure the following JS code is executed when the DOM is ready to be manipulated by JS
$(document).ready(function () {
  $("#newPassword, #confirmPassword").on("keyup", function () {
    // store the `newPassword` and `confirmPassword` in two variables
    var newPasswordValue = $("#newPassword").val();
    var confirmPasswordValue = $("#confirmPassword").val();

    if (newPasswordValue.length > 0 && confirmPasswordValue.length > 0) {
      if (confirmPasswordValue !== newPasswordValue) {
        $("#password-does-not-match-text").removeAttr("hidden");
        $("#submitBtn").attr("disabled", true);
      }
      if (confirmPasswordValue === newPasswordValue) {
        $("#submitBtn").removeAttr("disabled");
        $("#password-does-not-match-text").attr("hidden", true);
      }
    }
  });
});

и немного изменил ваш HTML на это:

<link
  rel = "stylesheet"
  href = "https://cdn.jsdelivr.net/npm/[email protected]/dist/css/bootstrap.min.css"
  integrity = "sha384-TX8t27EcRE3e/ihU7zmQxVncDAy5uIKz4rEkgIXeMed4M0jlfIDPvg6uqKI2xXr2"
  crossorigin = "anonymous"
/>

<script
  src = "https://code.jquery.com/jquery-3.5.1.slim.min.js"
  integrity = "sha384-DfXdz2htPH0lsSSs5nCTpuj/zy4C+OGpamoFVy38MVBnE+IbbVYUew+OrCXaRkfj"
  crossorigin = "anonymous"
></script>
<script
  src = "https://cdn.jsdelivr.net/npm/[email protected]/dist/umd/popper.min.js"
  integrity = "sha384-9/reFTGAW83EW2RDu2S0VKaIzap3H66lZH81PoYlFhbGU+6BZp6G7niu735Sk7lN"
  crossorigin = "anonymous"
></script>
<script
  src = "https://cdn.jsdelivr.net/npm/[email protected]/dist/js/bootstrap.min.js"
  integrity = "sha384-w1Q4orYjBQndcko6MimVbzY0tgp4pWB4lZ7lr30WKz0vr/aWKhXdBNmNb5D92v7s"
  crossorigin = "anonymous"
></script>
<script src = "./index.js"></script>

<form class = "form-signin needs-validation" novalidate>
  <div class = "card shadow-sm">
    <div class = "card-body">
      <div class = "form-group">
        <label class = "sr-only" for = "oldPassword">Current Password</label>
        <input
          class = "form-control form-control-sm"
          id = "oldPassword"
          name = "password"
          placeholder = "Current Password"
          required
          type = "password"
          autocomplete = "off"
          aria-describedby = "inputGroupPrepend"
        />
        <div class = "invalid-feedback">Please enter current password.</div>
      </div>

      <div class = "form-group">
        <div class = "form-group">
          <label class = "sr-only" for = "newPassword">New Password</label>
          <div class = "input-group">
            <input
              type = "password"
              autocomplete = "off"
              class = "form-control form-control-sm"
              id = "newPassword"
              placeholder = "New Password"
              aria-describedby = "inputGroupPrepend"
              required
            />
            <div class = "invalid-feedback">Please enter new password.</div>
          </div>
        </div>
      </div>
      <div class = "form-group">
        <label class = "sr-only" for = "confirmPassword">Confirm Password</label>
        <div class = "input-group">
          <input
            type = "password"
            autocomplete = "off"
            class = "form-control form-control-sm"
            id = "confirmPassword"
            placeholder = "Confirm Password"
            aria-describedby = "inputGroupPrepend"
            required
          />
          <div class = "invalid-feedback">Password not a match.</div>
        </div>
      </div>

      <p id = "password-does-not-match-text" class = "text-danger" hidden>
        Your new password does not match
      </p>

      <button
        id = "submitBtn"
        class = "btn btn-md btn-primary btn-block"
        type = "submit"
        disabled
      >
        Update
      </button>
    </div>
  </div>
</form>