Preventing form submission after validation by parsley.js

if you are using parsely 2 you can try this

$(function () {
//parsely event to validate form -> form:valiate
$('#rform').parsley().on('form:validate', function (formInstance) {
    //whenValid return promise if success enter then function if failed enter catch
    var ok = formInstance.whenValid()
    //on success validation
    .then(function(){
        alert('v');
        formInstance.reset();
    })
    //on failure validation
    .catch(function(){
        formInstance.destroy();
    });

$('.invalid-form-error-message')
  .html(ok ? '' : 'You must correctly fill *at least one of these two blocks!')
  .toggleClass('filled', !ok);
  // console.log(formInstance);
if (!ok)
  formInstance.validationResult = false;
  console.log(formInstance);
});

//parsely event to submit form -> form:submit
$('#rform').parsley().on('form:submit', function (formInstance) {
// if you want to prevent submit in any condition after validation success -> return it false
return false;
});

//default submit still implemented but replaced with event form:submit
$('#rform').submit(function () {
  alert('dd');
});
});

for more details parsely documentation check Form with examples and events

You are binding the submit event to a input element. If you check the jquery $.submit() documentation, it states that:

The submit event is sent to an element when the user is attempting to submit a form. It can only be attached to <form> elements. Forms can be submitted either by clicking an explicit <input type="submit">, <input type="image">, or <button type="submit">, or by pressing Enter when certain form elements have focus.

This is your main problem and this is why alert will never be displayed (in fact, that code is never executed).

I would also change a few things:

1. $('#rform').parsley( 'validate' ) should be $('#rform').parsley().validate(), assuming you are using Parsley 2.*
2. $('#rform').parsley( 'isValid' ) should be $('#rform').parsley().isValid().
3. Use $.on() instead of $.submit().
4. Remove onClickfrom the register_signup element. Since you are already using javascript, I would do this directly in the javascript code instead of onclick. This is more a personal preference.

So, your code will be something like this:

<form id='rform' name='rform'>
    <input id='reg_password' class='register_input' type='text'  autocomplete="off" 
        data-parsley-trigger="change" placeholder='Password' required>
    <input id='reg_cpassword' class='register_input' type='text' name="reg_cpassword"
         placeholder='Confirm password' data-parsley-equalto="#reg_password" required>

    <input id='register_signup' type="submit" value='Sign Up' />
</form>

<script>
    $(document).ready(function() {
        $("#rform").on('submit', function(e){
            e.preventDefault();
            var form = $(this);

            form.parsley().validate();

            if (form.parsley().isValid()){
                alert('valid');
            }
        });
    });
</script>