My family history goes back to the 1200's in Holland and the original farm still exists today. Both my parent naturalized in the sixties and became South African citizens before I was born. However my grandmother on my mothers side and both my grandparents on my fathers side were still Dutch citizens at my birth.
Would I qualify to apply for an ancestry Dutch passport and citizenship.
Almost certainly not. Your parents will normally have lost their Dutch citizenship when they naturalized in South Africa. Since that was before your birth, they would have had no Dutch citizenship to pass on to you. Your grandparents' nationality is not relevant.
However, there are various exceptions and corner cases whereby they might not have lost their Dutch nationality before your birth. I asked about some possibilities in a comment:
Was your father 21 years old or older when he naturalized? If not, did he naturalize independently of his parents?
To wit, if a minor naturalized independently from his or her parents, and the parents never naturalized or naturalized after the minor achieved majority, the minor's naturalization does not cause loss of Dutch nationality.
It's possible therefore that you might have been Dutch when you were born. If that is the case then you will also have to look into whether you have lost your Dutch nationality through one of the ten-year rules that have been in effect since 1985. That is why I asked when you were born.
Another reason to ask about that is that before 1985 Dutch nationality by descent could only be derived from the father unless the parents were unmarried. People who were born before then to a Dutch mother and her non-Dutch husband (which might include you if your father had lost his Dutch nationality but your mother had not) have a simplified "option" procedure available for acquiring Dutch nationality. A similar procedure is available to former Dutch nationals.
In conclusion, you may want to investigate a little more closely to establish exactly when your parents naturalized in South Africa.
