Christianity doesn't try to expand to fill law-making in the same way that Islam does.
The existence of the Vatican state today, and that of the Holy Roman Empire in Medieval times, I think proves you wrong.
Christianity has always attempted to impose itself in law-making and state politics, and was very good at doing so for almost two millennia. It just has lost (arguably) in Europe and in America in the last century, although it's still fighting for power whenever and however it can.
The existence of the Vatican state today, and that of the Holy Roman Empire in Medieval times, I think proves you wrong.
The Holy Roman Empire had a deal whereby you have worldly rulers on the one hand and the pope being the spiritual leader on the other hand. Popes supported the concept of the devine right of kings that was supposed to be given out by God to King David and passed down from David via inherentance to the present kings.
Islam on the other hand considers only God a valid source of laws and doesn't think that God has given human kings the r...
This topic is vague and open-ended. I'm leaving it that way deliberately. Perhaps some interesting, better defined topics will grow out of it. Or perhaps it's too far afield from the concept of less wrong cognition to be of interest here. So I view this topic as exploratory rather than as an attempt to solve a specific problem.
What useful purposes does religion serve? Are any of these purposes non-supernaturalistic in nature? What is success for a religion and what elements of a religion tend to cause it to become successful? How would you design a "rational religion", if such an entity is possible? How and why would a religion with that design become successful and serve a useful purpose? What are the relationships between aspects of a religion, and outcomes involving that religion? For example, Catholicism discourages birth control. Lack of birth control encourages higher birthrates among Catholics. This encourages there to be a larger number of Catholics in the next generation than would otherwise be the case, Surely there are other relationships like this? How do aspects of religion cause them to evolve differently over time?