I don't necessarily disagree with this, but I think the difference isn't between frontend and backend, it's between strongly typed and weakly typed, or structured and unstructured. The strength and weakness of Firebase and MongoDB is that they let you shove unstructured data into the db without defining a schema.
Once you have any users at all, you need to migrate that data every time your data model changes. When you need to migrate data, not having a schema goes from a blessing to a curse, because you're trying to change the structure of unstructured data.
For this reason, I'm skeptical of both sides of the coin. I'd almost rather start with an ephemeral in-memory store that forces you to rewrite before you have actual users, rather than be tempted by MongoDB or Firebase.