Interestingly, the guy who wrote NetNewsWire says Dropbox and RSS readers can't work together: http://inessential.com/2011/10/25/why_just_store_the_app_dat...
At some point I used RSSBandit (Open source desktop RSS reader for Windows), and I set up its %appdata% directory to be a subdirectory in the Dropbox folder. This can be done by modifying one of the config.xml files in the program's files. It worked. The whole state of the application was shared between computers.
Desktop app, synchronization between home and work, that was all I needed.