Just one thought on why it's also not my business, but I commented that I find it odd they won't say what type she has (or Charles).
They chose this life. Any born into it can abdicate and rightfully ask for privacy. Or Kate could not marry into it. But once you choose that life, in the words of Spider-Man, with great power comes great responsibility.
When they generically say "cancer," does any funding for cancer research see a significant spike? Does anyone learn anything from it that might help others? I'd argue not. With the influence they have and the ability to reach hundreds of millions of people, they should use that pulpit for good whenever possible. And if Kate has, say, colon cancer, then her saying that could lead to a significant increase in funding towards developing a cure for that cancer. It could educate people on the symptoms, and increase early testing. It could save many lives. So I'm just not moved by their "privacy" desires when they chose this life and could do something good.