Pouch, Firebase, and GUN[1] (disclaimer, I work there) are examples. If you bake permissions into the system itself, you get monoliths like Meteor. But you can still achieve granular permissions by rejecting/accepting network requests (like with ExpressJS or Hapi, etc.), which gives you the balance of using whatever backend you like.
Who wants to replicate their "whole" database locally?
So, probably no-one wants to replicate the whole database locally but there is a strong benefit to replicate parts of it for performance and offline-capabilities.
Disclaimer: I was one of two developers on the mobile app mentioned above.
What I actually want is MeteorJS with neither MongoDB or the JavaScript backend, or PouchDB without Couch, or Jaydata + ASP.NET WebAPI with more open source compatibility...
Is the syncing part as straightforward as Pouch[1]? I couldn't find anything about syncing on its docs. If a db comes with an easy offline-first and sync-when-possible model with granular permissions, it will be very interesting. Current solutions have (IMHO unacceptable) fixed dependencies on the backend or the architecture.
[1]: https://pouchdb.com/