Wow. Replying to myself. What is brought into question is the status of Proof by Contradiction, not the status of the Law of Noncontradiction. Russell seems to have confused these two things. And I don't blame him. It was 1940 after all, and there was a war on.

Another interesting fact. The book is built up from from accumulated material finally delivered over a course of lectures at Harvard University in a series called the William James Lectures in 1940 when England was at war but the USA was not.