To my knowledge, the Vedas do not propogate the caste. THere are references, such as my father priest, my brother carpenter etc which indicate that varna system, if present was not so rigid.
Regarding Bhagwad Gita, Krishna says do your swadharm, natural duty. He also says that certain qualities are predominant and one should do ones job based on your predominant type. It uses the words - gunkarma, based on qualities and actions. Not on birth, and actions is also stressed.
So a person simply born in a Brahmin family does not in any way make him special. His innante qualities and actions are important.
