The Dropbox API creates the 1PasswordSync
folder, whether you use it or not.
It cannot be deleted, but it can be hidden.
To do so, you will have to install DeveloperToolsCLI.pkg from Xcode (Mac OS Install DVD). Skip this step if you already have Xcode installed.
Next, launch Terminal
and enter the following command:
SetFile -a "V" ~/Dropbox/1PasswordSync
To unhide, simply replace "V" with lowercase "v".
This can be done on any given file/folder, and will only hide it on Finder view (Terminal doesn't care for Finder attributes, neither does Dropbox website or any other non-Mac app).