If you’d like to learn non-backwards-looking philosophy, which is indeed how most philosophy in mainstream American departments is done, then I highly recommend skipping undergraduate courses, which for some weird reason, kinda “talk down” to the students. Instead, I suggest three things:
(1) Just read the Stanford Encyclopedia of Philosophy. Pick a topic you like, such as causation or time or animal ethics, and just read the article or related articles.
(2) Read or skim academic papers or books. Most of them are surprisingly readable, especially the introductory parts. Notwithstanding criticisms of academic writing, I do think that analytic philosophy places unusual emphasis on writing clearly and plainly. (We can thank Russell and Moore for that in large part. Though, Plato wrote beautifully as well.) You can find good ideas for what to read from the Stanford Encyclopedia or track down philosophers whose work you find interesting.
(3) Listen to podcasts. Philosophy Bites’s archive is a treasure trove: it has so many important philosophers on and they all have interesting and clear explanations of some central idea. Also check out Matt Teichman’s elucidations. And there are a few more I’m forgetting. And then if you find something interesting, track the philosopher down, and read their books or papers. (Unfortunately, blogging by philosophers isn’t as active as one might wish; I think this tracks the general reduction in blogging on the Internet.)
You’ll learn a lot more this way than through undergraduate classes, which are usually slow and dull. I’m in philosophy grad school, but never took any philosophy undergraduate classes, but I picked up a significant background in philosophy using the 3 techniques above. I’m really happy for that. I love research-level philosophy, but undergraduate classes are too slow for me to sit through.
I don’t think one should see Pearl-type theories, which fall under the general heading of interventionist accounts, as reductive theories, i.e., as theories that reduce causal relations to something non-causal (even though Pearl might claim that his account is indeed reductive). I think such theories indeed make irreducible appeal to causal notions in explicating causal relations.
One reason why this isn’t problematic is that these theories are explicating causal relations between some variables in terms of causal relations between those variables and the interventions and correlational information between the variables. So such theories are not employing causal information between the variables themselves in order to explain causal relations about them—which would indeed be viciously circular. This point is explained clearly here.
If you want a reductive account of causation, I think that’s a much harder problem, and indeed there might not even be one. See here for more details on attempts to provide reductive accounts of causation.