My Christian grandfather describes astrology as "God's way of showing us His plan for our lives." And indeed there are quite a few passages in your bible that support that idea.
You're wise to ignore "horoscopes" as they're only a small portion of astrology, and thus not able to be accurate to the individual. :) For those who have not explored the subject, horoscopes are not all there is to astrology. Horoscopes only deal with a tiny part, the Sun, because that fits best in a small space and is easiest to look up. Astrology does NOT try to fit everyone into 12 boxes, and far from being purposely vague, most of you would be surprised by its complexity. A full astrological chart is based on the date, place and exact time of birth and you have a minimum of 7 planets, 12 signs and 12 houses, and the geometric relationships between them, as well as transits and progressions. Actual astrology is so complex that no one else will have the exact same chart as you do for millions of years.
Contrary to popular belief, it has never been "debunked" by science because the ones trying to debunk it stop at the newspaper columns and never explore the subject in its entirety. In fact, most of the arguments used against it show a total and utter lack of understanding of what astrology actually is and what it actually does. (We know all about the two different zodiacs, we know about the Precession of Equinoxes, the geocentricity is because we're born on Earth *not* because we don't acknowledge the Sun as the center of the Solar system, there is no 13th sign because zodiac signs are *not* the same thing as the constellations bearing the same name, etc.) And we also count among our number several doctorates and other highly-educated people who learned it so they could disprove it and found they were unable to.
Astrologers will differ on the hows and whys of astrology. I can only speak for myself. The stars do not make anything happen to you, they're only reflecting what is already happening via synchronicity. A good analogy is that a clock striking noon doesn't make you eat lunch, but it does make it a lot more likely than lunch will be had. I do not believe that astrology can predict specific events, only archetypal themes that will be in play. A particular aspect can play out in an infinite number of ways, but it can not "just mean anything," it will stick to the archetypal themes of the planets, signs, houses and aspects involved. Many psychological concepts, such as the midlife crisis, have an astrological correlate.
So in closing, astrology is not about "fortune-telling" or denying your belief in God-given free will. The chart shows potentials and themes, not "fate." It is not about "star-worship" or demonic influences; astrology is a neutral tool that can be used by people of any religion or no religion. In the modern era, it's much more akin to psychology and self-analysis than anything else.