"Ein mazal leyisrael" – "There is no constellation determining the fate of Israel" (Shabbat 156a)
This quote implies that the destinies of non-Jews ARE in fact determined by alignments of the stars and planets. This is just one of many places where Chazal display a belief in astrology. This belief carried on to many of the later rabbis – not only those who insisted on taking every word of aggadta as scientific truth, but also many of those who did not (for one example, see Ibn Ezra on Devarim 4:19). Rambam is a conspicuous exception (see here), but he is the exception that proves the rule.
The question arises: how are we supposed to respect religious authorities who believed something which is so clearly illogical, superstitious, and compatible with idolatry and rejection of Divine providence?
I think the answer is to argue that astrology was unsuccessful science, not pseudo-science. Astrology started with correct observation of some situations, and extrapolated to other, similar, situations. The data and conclusions were lacking, but the method was correct even by modern standards.
For the fact is that certain heavenly bodies do strongly influence events on earth. The best example is the sun. On a daily basis the sun's position determines the temperature and the amount of light we see. Over the course of months, as the sun's position in the ecliptic varies, other changes take place. Not only is weather affected, but in particular seasons plants grow, flower, and bear fruit, and in springtime most animals give birth. The moon affects the world as well, through the tides. Given all this evidence, can we not extrapolate and say that other, smaller heavenly bodies should have more subtle effects on earthly events? Particularly as those bodies (planets) have complicated and non-regular (as seen from earth) orbits, which correspond to the irregularity of life as we experience it?
Of course, modern science has found more precise theories to explain those situations. The sun releases radiation due to its high temperature, which warms air and water to create weather, and various life forms have adapted their life cycle to the regular changes in sunlight and weather. And any sufficiently large body has the power to create tides: if "Yo Mama" (the technical term for an extremely overweight person) were to go to the beach, the tide would rush up to meet her. Modern science allows that Jupiter and the Great Dipper have some influence on us, due to their gravity and radiation. But of course, practically speaking, that influence is completely negligible.
Nowadays, since we possess better scientific explanations, astrology is taken seriously only by idiots and frauds. But it's not fair to say the same about people who lived before the time of Isaac Newton, more or less. Until then, astrology provided the only plausible explanation for many natural phenomena, and there is nothing strange about its being almost universally believed and accepted.