Brent Simmons explains how RSS synchronization would work if you wanted to use five different RSS-reading apps on different devices. It sounds like a nightmare. I would never ever in a million years attempt to develop this. It's a million times more complex than RSS itself. Bad use of your energies as a developer.
Sometimes you just have to say no to users. No, we don't do that. If you want that feature feel free to get X, where X is the name of an app that promises to provide the annoying functionality. Especially when there's such a simple solution to the problem that requires the user basically giving up nothing.
For 10 points, what's the solution? Expand this heading on the story page for the answer.
PS: I had lunch today with Chris Anderson of CouchBase. I bet he'd say you could do a fine job of sychronization with CouchDB.