Given some of Noonan's methodology and conclusions in his books, I would think that more traditional Catholics* would shy away from him. For a few examples, in his book Contraception Noonan omits oral tradition from the list of resources that early Christians used to form their views on contraception, said that Stoicism had a "profound" influence on Christian thought on the topic, and also pointed out that Augustine condemned the ancient version of NFP. In another book of his that I've read, A Church That Can And Cannot Change, he seemed to argue that Christian morality has changed over time, a position I imagine many more traditional Catholics would disagree with. Yet I see Noonan's name brought up from time to time by Catholics, especially in discussions on contraception, when he is treated like an authority. What, in general, do more traditional Catholics think of him?
* By "more traditional Catholics" I merely mean those who take their Church and it's teachings seriously, attend mass regularly, support the Church on issues like contraception and a celibate priesthood, etc.
EDIT--While I don't own either of the two books mentioned anymore, I can still provide references (and in some cases full quotes) for the claims made in regard to Noonan's book on Contraception, if someone wants them. I'm afraid I didn't save any references or quotes from the other book.