Good news, everybody! You can now mark categories as private, on public sites. This feature is available for all wikis (free and pro). Note that you can't make the default category private, mainly because that would just give you a private wiki, which is still a pro feature.
This is still a basic version, and members of a site can easily break the privacy by e.g. using ListPages or includes. However it lets you create private spaces for the members of a site to work together on parts of a project.