I like this. I have trouble seeing a Liberal Judge raiding the courthouse with a shotgun. They're useful people to know (very good sleepers) but heavily invested in working within the system. The LCS has more ambitious goals.
One logical place for it to come into the gameplay is the "Stay at (location) as a sleeper/Join the active LCS" decision. If Wisdom > your recruiter's Persuasion, or 2*Wisdom > your Persuasion + their Heart, or some such constraint, you don't get the second option. (Of course you can always recruit them out of hiding later, once you gain a few points of Persuasion.) Conversely, high Wisdom ought to protect sleepers from getting caught, because, again, they know how to work within the system.
I
do like this, though I'm not willing to give up on Wisdom as acceptance of Conservative ideology and framing (as well as a certain degree of callous self-interest) as a foil to Heart's Liberal ideology (as well as senseless empathy). Tying these values (selfishness vs. empathy) to specific political ideologies is very much in keeping with the idea that this is to be a political satire, and by leaving it as two stats instead of one, you end up with engaged Moderates who understand both well needing to have one of the two refuted to make them choose sides, whereas those Moderates who don't care about either are just plain apathetic until a convincing case is made for one ideology (even if the other ideology isn't explicitly denounced).
Make a new stat for it and call it Radicalism or Conformity; this could replace the profession-based recruitment difficulty differences which currently present a limited version of the same idea. A CCS Boss would have a massive Radicalism (or if you prefer, minimal Conformity), whereas pretty much every other Arch-Conservative (and e.g. Judges/Lawyers/Police of all alignments) would have the opposite. It pretty much boils down to "how much you buy into the existing system". If you have a comfortable place in it, you can't be arsed to give up your job and go live in a homeless shelter (let alone assault the local precinct) just to make the country meet your political ideals; that's what voting (or at absolutely most, clandestine activism w/o radically changing your lifestyle) is for. If you're a social reject/dropout, you've got less invested in maintaining the status quo, and also less to lose by sudden, massive changes in your life.
A good Conformist would also be better at persuading/recruiting other Conformists, and worse at snagging Radicals. This could (sensibly, IMO) make it a bit harder for e.g. the Janitor to flip an Anchor or CEO; if you want to get someone like that you probably need at least an Office Worker, if not a Corporate Manager. Conformists would probably also do a better job at recruiting new sleepers than new active members, and vice versa with Radicals. Artisanal "re-education" would presumably completely Radicalize someone.
(Radicalism would definitely do well to be modified by Juice/Balls/Whatever; nothing encourages a non-conformist lifestyle like living it. It'd also mean that having that News Anchor filling your head with Conservative ideas could indirectly make you less Radical, and more likely to pine for a cubical. Hmm... this is a good point. If we're looking at Radicalism as being a means to determine if you'd do risky/violent actions, having the Police Negotiator crushing your Juice would make it more like to push your Radicalism down (or Conformity up) to the point where you'd be more likely to surrender, which would naturally be the less Radical course of action when confronted by Police. However, your average e.g. Gang Member who was extremely Radical to start with is probably still going to be too Radical to give up, unlike, say, that nice Conformist Programmer.)