[Vuejs]-Including script tags inside element Vue vm is binding to throws template error

This is because of the <script> tag inside your #app div.

<script>
    function onSubmit(token) {
        $("#register-form").submit();
    }
</script>

You should move this to the end of the document with the other JS.

EDIT

Alternatively, you might look at something like this to allow you to add scripts to Vue components.
https://github.com/TheDynomike/vue-script-component

Then you could create a Vue component for each ad script, which you could drop into the page where you need it.