In category theory, you often run into what is known as "size" issues. That is, you run into the issue that the categories you try to define are too "big" to be sets, and so you need to use classes or even larger collections. There are a couple solutions, but one of them would be to use NF or NFU. Since they have a set of all sets, you do not need to worry about your categories being to big. Having a category of all categories which is an object of itself is no problem, for example.
My question is, are there any issues with NF or NFU that would make them problematic as a foundation for category theory. If so, what are these issues?