How did the reaction of many southern whites to the civil rights activities ironically serve to the blacks' cause? how did blacks respond when it became clear that the legislative victories of 1964 and 1965 were not enough to satisfy their aspirations?

Their reaction was ironic because they were being violent. In their fighting against the African-Americans they actually got more people to join the African-Americans since they used such violent methods that they were disliked by absolutely everyone which meant that their methodology was extremely counter productive.

Their aspirations were to have equality in the society and this wasn't achieved with just those two acts. Segregation in school and housing was still high because desegregation was going at a snail's pace so they started voting more and electing black officials as well as going to courts more to fight the problems. This resulted for example in the Fair Housing Act which came out in 1968.