Try not to see security from the developer's point of view, but instead, follow a set of best practices. For example, you will be accepting input from a user, in the form of a file upload or text input, sanitize the content nonetheless, look at the answers to this question for tips on how to sanitize user defined css.
I would not assume that the css may only come from the user who will see it, this is most likely the current requirement, but I would not be surprised if in the future, a series of changes would allow this restriction to be bypassed.
Also, depending on the implementation (for example if you serve a url to a css file) someone may be tempted to try to just change all the urls for a malicious one (http://good-site.com/user1.css --> http://bad-site.com/?inject=user1.css), think XSS, injection, etc...
In short, my advice is to implement all security measures available given your project constraints.