Some basics from the book.” Who were the Shudras” by Dr B R Ambedkar, excerpts, as follows.

The Shudras are said not to have the right to study the vedas. How is it then that Sudas, a Shudra, was the composer of the hymns of the Rig Veda.
The Shudras are said to have no right to perform sacrifices. How is it that Shudras performed the Ashva-Medha sacrifice ? Why does the Satpat Brahman treat the Shudra as a sacrificer and give the formula of addressing him ?
The Shudras are said not to have the right to Upanayana.If this was so from the very beginning, why should there be a controversy about it ?Why should Badari and the Samskara Ganpati say that he has a right to Upanayana ?
The Shudra is not permitted to accumulate property.How is it that the Maitryani and Kathaka Samhitas speak of the Shudras being rich and wealthy ?
The Shudra is said to be unfit to become an officer of the State. Why is it then the Mahabharat speaks of Shudras being ministers to kings. There many such riddles unattended by the scholars and the society.Dr Ambedkar has dealt with the riddle very exhaustibly in his above mentioned book. It is the callous attitude of the society which is responsible to perpetuate this malaise. Even the Government shall take note of only when the society prevails. Let us bring about the change by organizing an introduction to Sanskrit to the most deprived of the Shudras and organizing an Upanayana sanskar for them.