They still have control over their data. If implemented properly, it just changes where there post is created since the post is synced back to their own server to their own account. Regardless of where it was created, it would still be visible on that server since it is a reply to that post.
And you also have to consider how other platforms treat upvotes and downvotes.
On many platforms, your upvotes and downvotes are not only visible, but sometimes result in a notification alert (i.e. someone commented on your post, someone liked your post, someone downvoted your post, etc.). It is not anonymous at all.