Q: Does astrology determine destiny? Is there a difference in this respect between a Jew and non-Jew?
A: There is a difference of opinion in the Talmud as to what factors determine a Jew's destiny. The accepted opinion is that ein mazal l'Yisrael, the stars do not determine a Jew's destiny.
The Ba'al Shem Tov explains that ein mazal l'Yisrael is to be read aiyin mazal l'Yisrael. The fate of Yisrael is the Divine state of "Nothingness." The fate of all other mankind is a state of being. Every non-Jew has a fate which is from destiny. Whether inscribed in the stars or some other dimension of reality is not significant. There is some fate which is almost impossible for the non-Jew to overcome.
A Jew, on the other hand, can overcome his mazal. This is because the origin of his fate is the "Divine Nothing" itself which is not well defined, as it is from the essence of G-d which is also not well defined. Just as G-d cannot be defined, so the destiny of a Jew cannot be defined. This is what is meant by Aiyin, "nothingness" is the mazal of Israel.
On every birthday the mazal of a person becomes stronger and shines from the super conscious level of the root of his soul into the consciousness of his soul. The mazal gives him strength to use to the maximum his power of free choice. This is just the opposite of thinking that mazal is not free choice.
In his book Etz Chaim, the Arizal explains that non-Jewish astrology only reaches a certain level of the 12 constellations or signs of astrology, but there are many levels above this. The highest of all levels are the 12 permutations of G-d's Name, Havayah. Only the Jewish People are connected to this level. By being connected to this level they have the power to re-create. (The Name Havayah means "continual creation".)
Astrology is very limited. The Torah and the Jewish People transcend this limitation of the non-Jewish astrology. When something is transcended it doesn't nullify its abstract source. Transcendence occurs by reaching the abstract source. That is what the Ba'al Shem Tov meant when he said that Israel's mazal is aiyin.