Dammit, I typed out a whole answer to your question and then saw that you were asking specifically about modern American culture, which I have no specialization in. My undergrad degree, 15 years old, is in History of Science, with a focus on the medieval and renaissance west (including muslim cultures). In case it's of interest, my further-back-in-time focused answer is:

Astrology has been with us for a very long time, and, along with navigational and timekeeping purposes, was one of the primary reasons that the ancients studied the stars. Remember that the concept of the Scientific Method is really pretty new, and that in the past, different paradigms for understanding the universe and our place in it were dominant. I'm not too sure about the Greeks and Romans, but there are many examples of Medieval and Renaissance Christian and Muslim rulers who kept astrologers on staff to try to divine, for example, when the most auspicious time was to undertake a certain action. Throughout the period, there are examples of astrology naysayers, people who expressed their doubts that God's will could really be revealed in such a way, but they in no way formed what we might today call a scientific consensus. The concept of scientific consensus is also newer, and the closest medieval European analogue would probably be doctrine handed down from the Pope. From my limited recollection of the status of scientific inquiry in China around the same time, the situation was pretty similar.

The book "God's Philosophers: How the Medieval World Laid the Foundations of Modern Science" (James Hannam, 2009) explains how a mid-16th century thinker named Jerome Cardan used the then-embryonic scientific method to try to compile a Grand Unified Theory of astrology, gathering the charts of as many people as he could to try to extrapolate some overarching rules. He found none, so it could be said that this marked the end of astrology being accepted as anything near scientific consensus.

I'm not too clear on why so many people continue to buy into astrology, except that as many other recent examples show, there are always going to be people who reject scientific consensus and in some cases even the scientific method itself.

Some other books you might want to look at: God's Philosophers (mentioned above): a bit pop-hist, pretty easy reading, drives hard its thesis that Renaissance Humanism actually caused setbacks in the cause of understanding the world through a scientific lens "The Foundations of Modern Science in the Middle Ages: Their Religious, Institutional, and Intellectual Contexts", Edward Grant, 1996, and "The Beginnings of Western Science: the European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450", David C. Lindberg, 1992. My introductory level university textbooks in History of Science. Presumably cover many other topics in this subject matter besides astrology, but I haven't read them in 20 years. "Aladdin's Lamp: How Greek Science came to Europe Through the Islamic World", John Freely, 2009. Plenty of examples of rulers employing court astrologers, what those astrologers did, and how their pursuit of astrology nonetheless advanced our state of astronomical understanding "The Duke and the Stars: Astrology and Politics in Renaissance Milan", Monica Azzolini, 2013. A confession: I haven't actually read this one yet, but it looks like it's more directly on point for your question than the other works I mentioned.