Rambam repudiates astrology, writing that only fools believe in astrology (Hil. Avoda Zara 11:17-8):
יז ודברים האלו--כולן, דברי שקר וכזב הן; והן שהטעו בהן עובדי עבודה זרה הקדמונים לגויי הארצות, כדי שיינהו אחריהן. ואין ראוי לישראל, שהן חכמים מחוכמים, להימשך בהבלים אלו, ולא להעלות על הלב שיש בהן תעלה: שנאמר "כי לא נחש ביעקוב, ולא קסם בישראל" (במדבר כג,כג), ונאמר "כי הגויים האלה, אשר אתה יורש אותם--אל מעוננים ואל קוסמים, ישמעו; ואתה--לא כן, נתן לך ה' אלוהיך" (דברים יח,יד).
יח כל המאמין בדברים אלו, וכיוצא בהן, ומחשב בליבו שהן אמת ודברי חכמה,
אבל התורה אסרה אותן--אינו אלא מן הסכלים ומחסרי הדעת, ובכלל הנשים
והקטנים שאין דעתן שלמה. אבל בעלי החכמה ותמימי הדעת, יידעו בראיות
ברורות--שכל אלו הדברים שאסרה תורה, אינן דברי חכמה, אלא תוהו והבל
שנמשכו בהן חסרי הדעת, ונטשו כל דרכי האמת בגללן. ומפני זה אמרה תורה,
כשהזהירה על כל אלו ההבלים, "תמים תהיה, עם ה' אלוהיך" (דברים יח,יג).
These practices are all false and deceptive and were means employed by
the ancient idolaters to deceive the peoples of various countries and
induce them to become their followers. It is not proper for Israelites
who are highly intelligent to be drawn by such inanities or imagine
that there is any benefit in them, as it is said "For there is no
enchantment with Jacob, neither is there any divination with Israel"
(Numbers 23:23; and further "For these nations that you are to
dispossess hearken to the soothsayers and diviners; but as for you
"The Lord your God has not suffered you so to do" (Deut. 18:14).
Whoever believes in these and similar things and, in his heart holds
them to be true and scientific and only forbidden by the Torah, is
nothing but a fool, deficient in understanding, who belongs to the
same class with women and children whose intellects are immature.
Sensible people, however who possess sound mental faculties know by
clear proofs that all these practices which the Torah prohibited have
no scientific basis but are chimerical and inane; and that only those
deficient in knowledge are attracted by those follies and, for their
sake, leave the ways of the truth. The Torah, therefore, in forbidding
all these follies, exhorts us, "You shall be wholehearted with the
Lord your God (Ibid 18:13)" (Trans. based on R. Dr. Twersky; A Maimonides
The list of forbidden activities he is repudiating at the end of the chapter, includes astrological predictions, as in halakha 9)
Elsewhere he also references "the stupid astrologers" (Hil Teshuva 5:4):
כמו שבודים מליבם הטיפשים הוברי שמיים
Rambam wrote a letter on astrology cited and translated here (original Hebrew text here in which he writes:
Know, my masters, that every one of those things concerning judicial astrology that (its adherents) maintain—namely, that something will happen one way and not another, and that the constellation under which one is born will draw him on so that he will be of such and such a kind and so that something will happen to him one way and not another—all those assertions are far from being scientific; they are stupidity.
Nevertheless he believes that the constellations are more than just stupid rocks. (Cf. Hilchos Yesodei Hatorah 3:9). They are channels for divine intervention in the world.
Just as we maintain that the Holy One, blessed be He, performs signs and wonders through the angels, so do these philosophers maintain that all these occurrences in the nature of the world come through the spheres and the stars. They maintain that the spheres and the stars possess souls and knowledge. All these things are true. I myself have already made it clear, with proofs, that all these things involve no damage to religion. And not only this, but what is more I have understood from the sayings of the sages in all of the Midrashim that they maintain as the philosophers maintained. There is no controversy whatever between the sages of Israel and the philosophers on these matters.
Rambam's main point is that ultimately the goings on in the world are exactly in line with God's will in response to our good or bad behavior, and no other entity calls the shots. (This seems pretty similar to Ramban's statement in the end of his commentary to parshas Bo that our goal is to realize that ultimately God pulls the strings on everything in life).
The controversy lies in this, that the true religionists, and that is the religion of Moses our Teacher, maintain that what happens to individuals is not due to chance, but rather to judgment... This is a root of the religion of Moses our Teacher, that everything happening to human beings is a (just) decree and judgment. Hence, the sages maintained: "There is no death without sin and no affliction with transgression" (Shabbat 55a).
He further emphasizes that man has absolute free will.
Every action of human beings is left to them and that there is nothing to constrain or draw them. Rather, if he so pleases, a man will worship God and become wise and sit in the house of study. And if he so pleases, he will follow the counsel of the wicked and run with thieves and hide with adulterers. There is no influence or constellation under which one is born that will draw him in any manner toward any one of these ways. Hence it was commanded and told to him: "Do this and do not do that."
In regard to the position of the Rabbis he writes:
I know that you may search and find sayings of some individual sages in the Talmud and Midrashim whose words appear to maintain that at the moment of a man's birth, the stars will cause such and such to happen to him. Do not regard this as a difficulty, for it is not fitting for a man to abandon the prevailing law and raise once again the counterarguments and replies (that preceded its enactment). Similarly it is not proper to abandon matters of reason that have already been verified by proofs, shake loose of them, and depend on the words of a single one of the sages from whom possibly the matter was hidden. Or there may be an allusion in those words...
Note that Rambam doesn't quote the astrological advice about Mars from the Gemara in Shabbat, even though the Gemara expresses no doubt about it.
Elsewhere he emphasizes how unreliable astrologers are (Yesodei Hatorah 10:3).
He further writes in his Iggeret Teiman (quoted here).
I note that you are inclined to believe in astrology and the influence of the past and future conjunctions of the planets upon human affairs. Dismiss such notions from your mind. Cleanse your mind of them as one cleanses dirty clothes. Accomplished gentile and certainly Jewish scholars refuse to believe in the truth of this science. Its postulates can be refuted by real proofs on rational grounds, but this is not the place to enter into a discussion of them. (Halkin translation, p. 116)
R. Qafih concludes that according to Rav Saadya Gaon (cf. commentary to Iyov ch. 39 pp. 194-5 and commentary to Exodus 21:13), the Hovot HaLevavot (Shaar Yihud HaMaaseh ch. 5 in ed. R. Qafih), Rabbi Yehuda HaLevi (cf. Kuzari 1:1, 4:23), and Rambam (see above and Shemonah Ferakim ch. 8, and Moreh Novokhim 3:29), astrology is meaningless and forbidden. (Ketavim Vol. I p. 93). R. Qafih's own approach is to follow Rav Saadya Gaon, Hovot HaLevavot, Rambam, and the rest of that school. In this vein, he discourages use of the expression 'mazal tov', as it is astrological, as does his student R. Ratson Arussi.
Without a particular source (yet) I imagine that later thinkers would not agree to the point that the celestial bodies have intelligence. This may well have been a medieval belief that was reverse engineered into Jewish sources. They would presumably agree to his core points that man has free will to do good or bad, and that God will is expressed fully in the world through whatever media he desires.
For more sources see here. See also here.