Posts always need to be assigned to an author. So what I’d suggest is create a user in your admin to whom these posts will be assigned – Anon User – or whatever you’d like to call them. Remember to make sure they’re of the correct role to publish posts.
Then in your
acf_form function, specify this user to be the author of that post. In the args for your form, just add
'post_author' => 123 – where 123 is the ID of the user you’ve created.