But is it OK to say: I wish you were never like me OR do I have to say I wish you were not like me?
You wrote that: wish ... would never ... is not an idiomatic combination, but does it mean that saying I wish you would never be like me is simply wrong or just sounds strange, but is not incorrect?
Both would never be like and were never like raise the same objections. The problem is never. wish introduces a counterfactual, and it's hard to see what, exactly, is being countered.
I wish you were never like me, but in fact you are always like me? I wish you were never like me, but in fact you are sometimes like me?