Conservative Public Theology is based on a vision of fixed, stable, traditional social order where everything works as it should. The old school bases this vision on religion; the new school on the invisible hand of the market. When the world doesn't work as it should, it is because individuals have failed to live up to it. They have sinned.
According to conservative public theology, the Las Vegas insurrectionists became bad people. Yes, they were good people a while ago, when they rallied for Cliven Bundy, but since then, they became bad people. It is good that they died. They are responsible for what they did; no one else.
Liberal Public Theology is based on an understanding of society and cultures as growing, evolving entities. They have the capability of progressing. When cultures progress, the behavior of individuals change. So liberal public theology is concerned about structures and systems more than individuals. So when liberal public theology looks at these Las Vegas commandos, they ask where did their ideas come from? what difference does it make that guns are so available? What are the systems and structures that lead to young people declaring war on this government and becoming cop-killers.
Liberals will ask conservatives to take responsibility for setting the stage for this deadly skirmish in an imaginary rebellion. Conservatives will be shocked that they should take any sort of responsibility for the actions of others, even some of their own. After all, they will say, "I didn't shoot anybody. I don't think the police are Nazis. Just like I didn't own slaves, nor did I lynch people, nor do I rape women, nor do I harbor ill will toward the poor people I know". The very essence of conservative public theology denies the very concept of social responsibility for anything.
Liberal Public Theology, especially as articulated by Unitarian Universalists, is based on three fundamental points -- each of which is denied by conservatives.
One is that every person matters, has worth and dignity, and can therefore never be discarded. No matter what they do, or didn't do, we still have to care about them.
Conservatives believe that those who do not exercise personal responsibility deserve whatever they get. The rest of us do not need to think about them again. Send them to jail; make her have that baby; let them die in the emergency room if they didn't buy insurance; let them starve if they are not working.
The second point of liberal public theology is that everything causes everything else. Everything is interconnected and interdependent. Everything is in a context, part of a system and structure.
Conservatives believe in individual personal responsibility and individual judgement. To them, some people are bad, demonic, in the grip of the sins of lust, or sloth, or greed. They have no one to blame but themselves, and they must face the consequences. None of the rest of us are responsible for what happens to them.
Finally, liberal public theology is evolutionary. The world was not in balance before human sin screwed it up. Humankind is advancing from a past which is cruel, exploitative, violent, and profoundly unjust. The world has never been fair, but it gets better.
For conservatives, humankind is miraculously self-correcting because it is innately functional. God set it up, and all we have to do is follow God's laws and all will be well. The secular version of that places the market in the place of God; everything will work out and come to balance if we do not interfere too much with the natural workings.
It matters what we believe.