Why were the jim crow laws allowed after the abolition of slavery?

The 14th and 15th Amendments to the US Constitution, enacted during the Reconstruction Era, already contained provisions to ensure equality of rights for all US citizens (including voting rights), without discrimination in terms on race. In practice, discrimination continued to be present not only in the society, but also in the legal systems of some states that legitimized practices such as segregation or that enacted laws to set limits to the voting rights of the African American sectors of the population, known as the Jim Crow laws. Such laws established requirements that citizens who wanted to vote needed to fulfill, for example, a minimum income requeriment or passing a literacy test. They did not explicitly exclude black citizens, as the requirements were set for everybody but the result of these measures was that large sectors of black people were mostly the ones who did not meet the standards and in turn, that could not vote.

The Jim Crow laws were allowed because, even tough their ultimate aim of preventing black citizens from voting was unconstitutional, the regulations that were actually implemented were not directly violating the US Constitution. It is true that many Jim Crow laws were subsequently interpreted to be unconstitutional by the US Supreme Court as they understood there was a discriminatory intention behind, but when one law was abolished a new one with a new requirement appeared rapidly.  

we will reach the goal of freedom in birmingham and all over the nation,