Following Thagard, I agree that Popper's criterion fails as a demarcation.
But let's look at other attempts at demarcating astrology as pseudoscience. Some have attacked it for its magical origins. But this doesn't work. The alchemical origins of chemistry are no reason to deem chemistry a pseudoscience.
Another failed attempt was criticizing astrology for its lack of physical foundations. This doesn't work. When Wegener proposed his theory of continental drift no mechanism was known at the time. Much of medicine have similar issues, we knew that cigarettes cause cancer even if we did not know, perhaps still not know, the mechanisms for how this happens.
Also doesn't work. Won't go into the details of why verificationist philosophy fails. One is that it rules out all of science as unscientific. Or another problem is that it rules out nothing. Anyway, astrology is testable so this criterion fails.
Okay now to the interesting view, that of Popper's. A Popperian would say that the problem with astrology is that it is not falsifiable. Since astrologers cannot make predictions which if unfulfilled would lead them to give up their scientific theory, then it is unfalsifiable, thus unscientific.
But falsificationist demarcation faces strong challenges as presented by Duhem, Quine, and Lakatos. These challenges Popper was aware of. He indeed said that no falsifying observation could guarantee the falseness of a theory. And the theory could always be rescued by auxiliary hypotheses. Popper would have us create a set of methodological rules to rule out this sort of ad hoc rescues. But Lakatos made a convincing argument that often theories ought to be rescued from hasty falsification. (Imre Lakatos, Philosophical Papers, vol. 1 Science and Pseudoscience)
Falsification only occurs when a better theory replaces the previous theory. But then falsification is then simply a matter of replacing a theory with another theory. And since in principle astrology can be replaced by another theory, falsifiability provides no criterion for rejecting astrology as pseudoscientific. Some would add that there are unsolved problems in astrology but this doesn't work either because even our best scientific theories have unsolved problems. Popper's criterion fails here. (Note that Popper's criterion works for universal law statements still, logic statements like all x's are y's)
So none of these work, what does then? Paul Thagard offers an interesting solution. One that has us consider a wider historical and social context. He proposes a demarcation of three elements, Theory, Community, and History.
In theory, we find the usual stuff, Prediction, Explanation, Parsimony. All the good stuff we might find in Popper.
He has us consider the community aspect of the advocates of a theory. First, are these practitioners in agreement on the principles of a theory and how to go about solving problems the theory faces? Second, do they care about anomalies in their theories? Third, are they actively involved in attempts to confirm or disconfirm their theory?
The final aspect of History relates to what Kuhn argued for that in general theories are rejected only when it has faced anomalies for a long period of time, and it has been challenged by another theory.
Thagard then proposes the following demarcation principle,
A theory or discipline which purports to be scientific is pseudoscientific if and only if:
1 it has been less progressive than alternative theories over a long period of time, and faces many unsolved problems;
but 2 the community of practitioners makes little attempt to develop the theory towards solutions of the problems, shows no concern for attempts to evaluate the theory in relation to others, and is selective in considering confirmations and disconfirmations.
Here it becomes apparent why Astrology fails. First, it has made little to no progress since the time of Ptolemy. Second, there are outstanding problems with no efforts to solve them, and more importantly, thirdly, there are alternative theories of personality and behavior which Astrologers are largely unconcerned with.
This is an interesting demarcation that borrows from Popper, Kuhn, and Lakatos. I think it works.