In Disintegrating the Musical by Arthur Knight, the author argues the opposite of this claim, and says the African-American reaction to Jolson's blackface act was mixed, at best, citing the Pittsburgh Courier as being highly critical while the Chicago Defender was a bit more sympathetic in the early "talkie" years. Knight's argument starts with the 1936 Pittsburgh Courier headline: "I Can't Believe Jolson Would Humiliate The Race".
Knight goes on to argue that the black community was more forgiving of his blackface act in The Jazz Singer due to the novelty of sound which gave many black audience members their first chance to see a white blackface act "relatively free from white surveillance" but thereafter, the African-American reaction to Jolson's blackface act became increasingly critical.
In The Talkies: American Cinema's Transition to Sound, 1926-1931 by Donald Crafton, the author is more circumspect, writing:
"How African-American audiences viewed...Jolson's films...and blackface comedies in general is difficult to know. The studios made these primarily for white audiences, welcoming any bookings from segregated black theaters as unplanned profit. But the extent of black attendance at these films is unknown" (emphasis mine).
In "Blackface, White Noise" by Michael Rogin, found in New Historical Literary Study: Essays on Reproducing Texts, Representing History, the author backs Knight's claim up:
"The original reviews of The Jazz Singer responded as much to Jolson's blackface as to [the] Vitaphone [sound system]."
In Street Scenes: Staging the Self in Immigrant New York, 1880-1924, author Esther Romeyn quotes some of these contemporary reviews, with one complaining the "minstrelsy of the blackface variety is supposed to reprsent a certain type of life and portray the characteristics of a race [but] seems to have been forgotten by the modern dabblers in this amusement", and another writing, "Mr. Jolson makes no attempt whatever to imitate a negro of any period or station in life...He is merely Al Jolson with burnt cork on his face..."
Roi Ottley's review for The Singing Kid in the April 11, 1936, edition of the African-American newspaper The New York Amsterdam News is more forthright:
"Al Jolson in blackface against a background of Negroes without make-up was a grotesque sight. We wonder when Hollywood will throw overboard such out-moded forms as blackface. Minstrelsy is dead as a theatre attraction."
Ottley writes that the main attraction of the Jolson film for the black audience he saw it with was for the chance to see black jazz bandleader Cab Calloway on screen. Jolson's "popularity" with black audiences may very well have been a function of his blackface act needing actual black faces behind it as supporting characters, so a Jolson film offered a rare opportunity to see African-Americans on screen in the early days of the "talkies".
There is an article entitled "Why Did Negroes Love Al Jolson and The Jazz Singer?: Melodrama, Blackface and Cosmopolitan Theatrical Culture" by Charles Musser, but as written about in the endnotes of Black Mirror: The Cultural Contradictions of American Racism, Musser's argument is only one view, and not one universally held.