Thought Experiment on Genetics and Society

I did something like this on Twitter, but will expand it here:

Let's say we live in a society where all the citizens are genetically identical (1 male and 1 female genetic code) and further that progeny, through laboratory manipulation or the like, retain the same genetic code from one generation to the next:

Will there still be a social hierarchy in such a society? Wouldn't a society require professionals and a working class. If it was along the lines of our current system, some would be doctors and some janitors and some field workers. Would those born to wealthy and well educated families have a leg up in also achieving educational and professional success? Might one also expect some homeless, some people with substance abuse problems, some people who are unhealthy? Some who turn to a life of crime? Some who would be humanitarians? Would there not eventually be wars and some way in which groups would be prejudiced towards other groups? Would people be more alike, or would they go out of their way to differentiate and be even more diverse in personality?

This is all quite obvious, isn't it? Gene hunting is not going to uncover human nature. We are human beings first. For the most part, genes simply display the costume that each of us wears. The exceptions to this fact are simply that: exceptions.  Marking people's personal traits by identifying generally unrelated genetic variations does little more than create meaningless divisions in our society and a perception of humans as genetic automatons.