I can speak of the German ones, CDU and CSU: the former is de facto Christian in name only, the latter is much more socially conservative, yet the Christianity-part is more seen as part of tradition - Germans don't go to church anymore, but celebrate Easter and respect all hallow's eve. Even the CSU has arranged itself with gay marriage, and abortion is traditionally a gray area in germany, and by god, they will keep it that way.
This allows them to argue that abortion is illegal, while at the same time not punishing it.
Mind you, the CSU is catholic, and catholicism is way more comfortable with ambiguity than protestantism, so this solution is fine for them.
Other than that, they are *slowly* becoming ecologically conservative - the CDU faster than the CSU, and are both highly neoliberal, economically.
So... the C in CDU and CSU is there to collect the remaining religious people, but in a way that shouldn't scare away non-religious social conservatives with neoliberal economic views.
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