Strong communities tend to have a shared religion but this doesn't tell us which way the casual arrow points. Given that trustingness is heritable, I think its likely that trustingness increases both religiosity and the ability to form a community. The sacrifice result seems a bit more robust since it was done with both religious and secular groups.

About liberals, they are the least accurate in modeling how other political groups describe themselves. However, this could mean that other groups are less genuine in their self description: for example conservatives that think that gays are gross will probably appeal to "family values" rather than being honest. And really all this tells us is that other groups are harder to understand. This doesn't tell us if they are right or not.