How to get the autocomplete feature for a taxonomy term profile field visible on the registration form?
Turns out it is a permission issue : adding the permission for anonymous users to View published content solves my problem as I do not have any reason to not let them see the website content

I guess for websites where content is for registered users only, this permission would not be granted and the widget would not be used on the taxonomy term field.. Maybe the Content Access module could help those use-cases