I was reading about the book, and I think it’s interesting that when it came out it was seen heralded as a great abolitionist book, and later civil rights groups decried it for racist stereotypes and the subservient Tom. How did Douglass or other black intellectual contemporaries feel about the book?
This was a complicated issue for radical abolitionists like Frederick Douglass, regardless of race. On the one hand, Uncle Tom's Cabin was an instrumental tool in creating public sympathy for the abolitionist movement and escaped slaves; on the other hand, not only was its portrayal of Black people based on minstrel stereotypes, but the 'solution' to slavery which UTC advocated was colonization in Liberia, a position which Douglass, Garrison, and other abolitionist radicals had long since repudiated.
Faced with this problem, abolitionist newspapermen like Douglass chose to chronicle the public response in the North and South and reluctantly avoid a direct critique of this potent antislavery weapon. Stowe's follow up text, "A Key To Uncle Tom's Cabin," directly utilized and repeated arguments from slave narratives like Douglass' own autobiography and abolitionist newspapers, which made it a more attractive tome for movement abolitionists than her bestseller. That said, after the Civil War was over, they had no compunction about attacking its failings; famously, William Lloyd Garrison was at an abolitionist reunion where Stowe was reading from Uncle Tom's Cabin and when members of the audience asked him to talk about its importance as an antislavery text, Garrison declared that Stowe's book's importance was overrated.
Its worth noting that Stowe's text was used to frame Douglass' public memory after his death, with a statue of Frederick Douglass, "as Uncle Tom," appeared at the 1893 Chicago World's Fair
Sources: Uncle Tom Mania: Slavery, Minstrelsy, and Transatlantic Culture in the 1850s by Sarah Meer
The Building of Uncle Tom's Cabin by E. Bruce Kirkham
Abolitionists Remember by Julie Roy Jeffrey