I'm not an expert in Third Reich history, but like you I was highly curious about this book when I read it in 2015. A quick search of JSTOR reveals that the Journal of Modern History Vol. 29, June 1994 (95-128) contains a review essay by Gavriel Rosenfeld which compares the reception of the book in the USA and West Germany upon its publication. He contrasts the reception in the US (wild commercial and critical success, best seller for over a year, etc) with that of its reception in West Germany (popular, but not as much, nor for as long as in th US). The book was seen as sparking a new wave of anti-Germanism in England and the USA and dangerous to the US-BRD alliance.

As you point out, the provocative thesis (Luther to Hitler thesis, so to speak) was also quite controversial. The thesis contrasted at the time with the totalitarianism argument, which located the origins of Nazism in a Europe-wide crisis of the interwar period, rather than any long-term, aberrant character of the German people. Rosenfeld shows how among the reviews of the book, historians were quick to point out that Shirer had not recognized this new scholarly paradigm. Rosenfeld also shows that this critique (of not recognizing the current totalitarianism paradigm) was also connected to political or patriotic sentiment, since the totalitarianism thesis also indicted Soviet Communism as emerging from the same crisis as German Nazism. While less common than the purely scholastic critique of the book's ignoring of the totalitarianism thesis, there did exist those reviewers who accused the book of being pro-Communist.

The article in discussion was written in 1994, and it focuses more on immediate reception of the book in the 1960s, rather than contemporary 1990s understandings of the book, but I think it helps frame some of the major historiographical issues of Shirer's book. Hope I've helped, and I hope some of our Third Reich experts come along and answer your question better than I have!