Of course it's entirely possible to believe in some semi-mystic ideas in the 24th century- take the spirit guide stuff from Chakotay , or the idea that the consciousness can be detached from the body - of course it helps that in the Trek universe there seems to actually be hard evidence for this idea (Cathexis). Coda shows us that there is still room for speculation about the afterlife. And so on. In fact I'd say there is a resurgence of such ideas in DS9 and VOY when compared to TNG.
But astrology in my eyes would seem particularly hard to defend, since (what I understand of it, which is admittedly not too much) it seems entirely based on how star constellations appear here on earth and on our local solar system, so I was curious how 24th century believers would explain that away when they can just go to another star system or interstellar space-- unless perhaps they would explicitly ascribe to the idea that all these "cosmic" astrological effects are just localised to the planet (or perhaps solar system) they are on.
Then again, people in our time also keep believing in certain 'alternative' ideas when science has already accumulated lots of direct or circumstantial evidence against and very little in support of those….