Is it established that personal success or happiness is primarily determined by personality and is largely independent of social identities?
This seems to me the old nature versus nurture debate and there is no real answer to this. However, I highly doubt that it is personality (as an inherent trait of you - nature) that's the most important factor for personal success. The question is what shapes your personality.

Family matters a lot, so building your personality over the right type of Childhood experiences seems to have strong effects on personal performance.

Yet, even such mundane things like names can have a huge impact on personal success regarding job oppurtunities.