There was a range of reactions from both the white and black communities regarding Booker T. Washington's famous speech, and they ran the full spectrum of emotion and reason.
There were those whites who, in their 1890s racism, felt it was presumptive and arrogant at that time for an African-American man to "agree" to segregation or anything else, as they felt it was above the social "place" of African-Americans to give consent or denial for any Jim Crow policy. Mostly, though, Washington's message was welcomed by white Governors and others in attendance at the conference, albeit under their breath, and his message was taken as permission from the entire black population to continue segregationist policies, and even to expand them.
There was more than a bit of aggravation among many blacks, including W.E.B. DuBois, who felt that the Compromise was in fact a sellout, and that Washington had no business speaking on behalf of all blacks in such a weighty matter as Jim Crow racism, and that the assurances of extra money for education Washington received were actually just "30 pieces of silver" to sell them all down the river. Some shared Washington's pragmatism in achieving what was socially possible at the time, and agreeing to a Jim Crow policy that was going to happen anyway, but they were in the minority.