Actually old suggestions refined a bit but anyway...
New issue, religion
Since many C+ laws are inspired by religion, having this issue C+ or C should naturally accelerate conservative ideas in fields such as abortion or gay rights. In a C+ religious society, Witchcraft is a serious offence, and results from doing anything with LARP stuff. Also, a couple of new characters to appear in conservative religious societies:
Witch - Liberal with average stats, high charisma (witch accusations were often made out of jealousy), start with Witchcraft crime flag.
Witch Hunter - Difficulty about SWAT-level. Armed, evil conservatives. Will invade safehouses that protect witchcrafters.
Crusader - Found loitering about randomly, or accompanying safehouse raids. The Christian equivalent to soldiers.
Monk - May be of any alignment. Master of martial arts. Sticks around but gets rare as society gets more liberal.
Military base
The driving force of the conservative raids, the Military base is packed full of fun!
- Recruits that may be anything from conservative to liberal (influenced by military spending) and anything from unarmed to hideously equipped (spending and gun control)
- Soldiers (you know them)
- MPs, deadly madmen armed to the teeth
- General Officers, with good combat skills and a persuasion attack
- Some random out-of-place civvies
- Distress signal - Activate the strategic bombers as they did in Dr. Strangelove!
Camp Jesus/Moses/Eliah/God/Conversion/Jehovah/Christ/Crusade/Crucifix/Chastity/Salvation/Virtue/Lazarus/Retribution/Whatever
Wanna smack the fundamentalists in the face?
- Children imprisoned in the camp by their parents, just waiting to be released!
- The aforementioned religious types
- Good old fashioned priests
- The occasional CEO, Radio personality or whatever dropping their kid off to conversion therapy to avoid public humiliation
- Security guards. You don't want the kids to escape, right?
Of course, the camp will remain the fortress of Fundamental Fun even after the society rejects its counterproductive commitments.
Game mechanics
Science, religion and business skills should give a boost to influencing related issues. Science works with GM, animal research, pollution, nuclear power etc, religion with abortion, gay rights, women's rights etc and business with labour rights, corporate laws etc. A new skill to give to the Generals and other such folk would be patriotism, which would suit military spending, gun control, immigration... The idea is that people with no knowledge of what they are fighting against are just shooting around when at the site. People who can truly reason why they did it are bound to gather more respect.
EDIT: Stealth action
When conservatives are unalarmed, a liberal may not provoke an alarm (immediately) when attacking a conservative. This works with melee weapons only, as gunshots can be heard. Chances of remaining undetected are determined by stealth skill and how quick the target dies (how many liberals need to attack before the target dies), with a penalty for each conservative witness (only real ninjas can do stealth hits in front of a crowd) and a HUGE penalty for using a non-concealable weapon (it's very hard not being spotted carrying one, let alone murdering with it). Also, any combat rolls against unalarmed conservatives should yield a surprise bonus.