I've been thinking about this idea at work lately. Here's another wall of text that also deals with only tangentially-related concepts:
There should be a 'Political Interest' meter (measured in percent) for each district, and also one for each generated individual (which takes the local interest level as its 'base' and then modifies it a bit depending on profession, age, stats and a certain random factor). The more affluent areas of a city will have a more politically engaged populace, both liberal and conservative. While going out on missions may change the stance of the politically aware part of the nation on many issues, it shouldn't actually make the oblivious more interested in politics for the most part (Radio and TV hijackings being the exception); you'd still need to find a more direct way to establish a link to your co-citizens and convince them to read more than just the sports pages of their newspaper. This can be done through various activities such as graffitti and liberal disobedience and whatnot. All of these activities should slowly raise the district's 'Political Interest' level.
Uninterested citizens will be much more difficult to engage in conversation (although seduction should not be affected), and convincing them to donate cash or join the LCS will also be much more time intensive (in fact, that is what the primary effect of those discussions should be: raising the interest meter with each successful meeting until the person is 'ready'). Interested individuals will have a higher chance of sticking around and fighting for their beliefs during conflicts (although nothing openly suicidal like an unarmed secretary charging a guy with body armor and an M4). The most important sign of an engaged citizenry is a high liberal turnout at the polls, less interested people will have a tendency to vote for the status quo, whatever that is at that point in the game (doesn't necessarily have to be conservative), or in extreme cases not to vote at all, which also helps the conservatives because they have more 'ideologues' to start with.
The industrial district is special in that it will be home to several gangs (although arch-conservative health care laws, if implemented, could turn the free clinic into an abandoned building for a gang to take control of, so the disease could spread to the wealthier districts as well). While they continue their activities, political interest in that district will steadily decrease (maybe with a small spillover effect for the other districts as well), as people have more pressing concerns (getting mugged on the way home, having their car stolen, having to ransom a kidnapped relative, being randomly murdered in the streets, etc.). Since political interest is essentially an effectiveness modifier for issues, your efforts in various courthouses and genetics labs will be noticed by a scant few until you tackle this problem. If you really want people to listen to your agenda, improve the neighbourhood! Bring change, not words!
Gangs could be dealt with in several ways. The most obvious way to remove a gang member from the equation is to beat him until his body dies. If you do this with enough gang leaders (or turns them into sleepers or whatever), the organization should collapse and disband. However, new gangs could surface if social conditions are unfavourable and not all turf is yet taken by others. Gangs could also split off from existing ones if there is internal strife (could be weak leadership, or unpopular rule changes). Another way to tackle the problem is by gradually convincing gang leaders to mend their ways. Each gang should have their own set of rules (once more about the gang is known, they could be displayed just like the current national law screen). For example, 'Robbery [Yes/No]', 'Drug Dealing [Hard/Soft/No]', 'Firearms [Illegal/Legal/No]', 'Kidnapping [Yes/No]', 'Community Support (amounts to looking after the wounded and the elderly of the group, but could be expanded by LCS intervention to non-members, too) [All/Gang/No]'. With enough respect and a high persuasion skill, the LCS could eventually 'pull' a gang towards the desired agenda and turn them into a beneficial factor.
A problem that comes up here is the game's binary friend/foe system. Gang members, unless encountered in a CCS hideout, are always Liberal or Moderate. It's currently not possible to target those, and if you hit them accidently, you would alienate a lot of people. I suggest an additional 'faction' tag that can be applied to any individual. If known by the LCS, it would appear to the left of their name in the encounter screen, and take the form of an ASCII symbol. For certain institutions, this symbol would be pre-set (the LCS should always be a green heart, the CCS always a red dollar sign), for randomly generated groups like gangs, the symbols should be random as well. The 'group tag', if present, should override political affiliation and allow 'duelling' for organizations known to be hostile towards each other with lower or no penalties. This will allow for gang fights and LCS action against them. I know that all of this is rather far-reaching, but I don't think that the idea goes against the character of the game because criminal gangs exist mostly for financial benefit, they are not born out of a political struggle like the LCS.