I love John Piper, as I assume has been evident over the years, but I found his answer to this question lacking at best and unhelpful at most. To some extent, he was directed to go to the biblical outline of gender roles by the phrasing of the question itself. But I think a better answer would be simply to step back, redirect, and consider the nature of a book. Any book. Any kind of book. Written by any author. Period. Female authors and male authors. Even Christian authors and non-Christian authors.
There is only one authoritative book. Every other book we can learn from and draw from and consider, testing all things its author teaches and clinging to whatever truth shakes out, even using what we see true in it in our life and ministry and public sermons.
I do subscribe to complementarianism, which means many things, one of which is that I agree with Dr. Piper that the Bible restricts pastoral authority in the local church to men. (Not just any men, of course, but those meeting the further qualifications for elder.) But the other key word in that phrase, the one that is not “men,” is “local.” Because of this, I don’t read any book, listen to any preaching, or otherwise gather any counsel outside of my church that I consider authoritative over me in the sense the Bible is concerned to restrict to only elders. Because I pastor a congregational church, all the members of my church, male and female, have in some sense authority over me. But only my elders have pastoral authority over me. This means that I don’t even read a John Piper book as if he has pastoral authority over me any more than I would read a Marva Dawn book as if she has pastoral authority over me. And I’ve read both and learned from both and used both.
Perhaps a better answer could have come from a better question. The better question is not “Is using a book by a woman a violation of the Bible’s restrictions on pastoral authority?” but “Is using any book a violation of the Bible’s restrictions on pastoral authority?” And the answer to both is “No.”
Now, of course, we ought to weigh some authors as more thoughtful, more faithful, more biblical than others, but I suppose that goes without saying.