Why was Zora Neale Hurston criticized in her lifetime by fellow African Americans for accepting endowments from white people who supported her?
In addition to the criticism for not writing protest literature, as ladyvols1 discusses very well, Hurston was also criticized more generally for her performance of black identity. Hurston was criticized by many black intellectuals and artists of her time for what they saw as her "playing the darky" to amuse and secure the support of whites.
For one brief discussion of this topic, see Nancy A. Walker's book A Very Serious Thing: Women's Humor and American Culture, p. 113. For another, see the web source cited below, on "The Problem of White Patronage: Charlotte Osgood Mason and Zora Neale Hurston." Wallace Thurman's novel Infants of the Spring offers a very developed and entertaining (although pretty mean-spirited) literary portrait of Hurston that, for me, captures the essence of this criticism of her.
Not all of the Harlem Renaissance writers wrote protest literature. Hughes consistently walked the line, for example; it may be fair to say that half his writings can be called protest literature. There's protest in Hurston, too (e.g. in her short story "Sweat" and in sections of Their Eyes Were Watching God).
Hurston wrote a great many stories, but she could not support herself on the money earned. Found herself having to live on funds given to her by patrons of the arts. There were white people who would pay for this "primitive art." "The stories that Zora wrote during the Harlem Renaissance were often criticized by the intelligentsia of the era because, as friend and fellow writer, Langston Hughes, stated, "[she] did not write fiction in the protest tradition"(Marks 59). Instead, Zora focused on what she knew of the southern Black existence and tried to create characters and story-lines that truly reflected black life." African-American authors during this period wanted "protest stories" about the hardships they had suffered under the white suppression.