A majority of the population is capable of casting cure minor wounds, which is enough to stabilize a dying creature. Most workplace injuries become irrelevant. Casualties in war drop as well.
They can also cast purify food and drink and create water. Starvation and thirst are reduced to almost a non-issue. Disease rates plummet since contaminated food is no longer a problem (even without taking into account the increased availability of neutralize poison and remove disease).
These two factors lead to a huge increase in population.
A large minority of the population can cast 1st level spells. Alignment detection may become commonplace, but it would be a gross violation of privacy. Still, it would certainly be used in trials, and as most governments would be theocratic, having an alignment contrary to the local deity's could be anything from a serious aggravant to a criminal offense in itself.
Having low Wisdom is now a serious handicap. People with a 9 would probably get to 10 as soon as they hit 4th level, out of social pressure. People with less than 9 have a real problem. Over thousands of year, a combination of education and evolutionary pressure could cause the race to have a +2 racial bonus to WIS (maybe at the price of a penalty to another stat).
Widespread literacy, required to become a cleric, would lead to great social advancements - but many theocracies stifle these. OTOH, a nation that follows a god related to progress, with most of the population capable of reading and writing, would develop rather quickly.
Low-CR undead are extinct in all places that don't like undead. Elsewhere, they are easily kept under control; you won't find ghoul-infested cemeteries in this world.
As for religious war; sooner or later, truces will emerge. I expect a period of strife, followed by the spread of religious tolerance for all cults that can reasonably accept it. The others will form their own isolated nations, providing trouble every now and then.