If Astrology is a science, it's not a science in the "orthodox", "establishment" sense, because that version excludes Astrology from its format. Waybread, since you know a lot of people in the modern scientific community, can you estimate how many of them accept it as a valid field of scientific study? One special case: I believe that mainstream Jungian analysts use astrology in their practice, and are themselves accepted by Establishment Science.
Astrology was considered scientific in centuries past, but it was always under scrutiny and criticism, even in the Greek and Roman worlds. This is why you see Hellenistic astrologers like Ptolemy and Firmicus Maternus going to considerable lengths to justify astrology to the sceptics. Part of the reason why astrology became a university subject in the Middle Ages was because of its affiliation with medicine.
The one astronomer I'm aware of who takes astrology seriously is Mike Brown, discoverer of some of the trans-Neptunians like Eris.
http://www.mikebrownsplanets.com/2008/01/i-heart-astrologers.html This isn't because he agrees with astrology's truth-claims; but rather, because he sees astrology as a cultural phenomenon with a poetic vision about humanity's relationship with the sky, and that shares a common history with astronomy.
Once the Copernican Revolution took hold and medicine began to make advances without the benefit of astrology, astrology's status as a science waned. The Copernican Revolution (ca. 1500) is really the beginning of the split between astronomy and astrology.
It is important to recognize that the science of the past is not the science of today. Science has evolved throughout its history, and we can't look at a past century as somehow typifying science in 2015.
Astrology today has very little in common with science. Science relies on the scientific method: hypothesis-testing, experimentation, data collection and analysis, and conclusions drawn from the results. This is usually done in a laboratory, observatory, or at carefully controlled field sites. Many disciplines are empirical, but we wouldn't call them science: like history, law, or accountancy, for example. The distinction between science and not-science isn't so much its factual basis (although astrology mightily struggles here,) but the methods employed. And astrology has yet to demonstrate its validity under scientific research conditions.
The scientific method is explained at:
http://www.livescience.com/20896-science-scientific-method.html and
http://www.sciencemadesimple.com/scientific_method.html
This just isn't what astrologers do.
So David, the number of card-carrying scientists today who except astrology as scientific today (not in the Middle Ages) would be extremely small. (I dunno, like maybe 2 or 3?) This doesn't mean that historians of science dismiss astrology as a cultural phenomenon, or as a part of science in the past. Historians of science have uncovered a lot of intriguing information about astrology at different times in the past. It is understood that a lot of good astronomy in ancient times and during the Middle Ages was conducted for purposes of astrology.
I can supply references if anyone is interested.
Jungian psychology is not mainstream psychology. I tried to look it up in university catalogues and in overviews of psychology some months ago, and found only two accredited comprehensive universities in the US that offered Jungian courses in the psychology departments. Jungian psychology is taught at specialized institutes, however. Some of them are approved by higher education accreditation bodies, and some are not. Today psychology is considered to be "behavioural science" and even has some overlap with neuroscience. Jungian psychology just doesn't fit this model, as none of it was based on controlled experiments. Actually, some of Jungian psychology is more akin to the humanities, with its emphasis on mythology.
I can't say how many Jungian psychologists use astrology in their practice. If you start googling these practitioners, I suspect that they would be in the minority. Liz Greene's psychology credentials were suspect, as her Ph. D. was from a short-lived "institute." When she recently returned to university (Bristol, 2010) for a credible Ph. D., she did not get it in psychology, but in history.
A few years ago a judge in India declared astrology to be a "science." This got the actual physicists, chemists, &c in India rather alarmed. The text of the judge's decision, however, reads more like a very loose definition of science that we see used in English, just meaning a body of knowledge of long-standing. In this sense, I might talk about the "science" of baking a cake. I personally don't mean anything physical or chemical about cake-baking, but more that there is a body of knowledge about baking, and the procedures can be exacting.