This is not universally true and individuals and societies don't have to be organized this way.
Why are streets in some countries filled with trash when others are clean? My community does not have anyone policing littering - yet our streets, parks and public areas are litter free.
This isn't true of everyone, but assuming it is increases the likelihood that it will become so. Because if everyone is trying to get away with it, why shouldn't I? That sort of breakdown in trust is high up on my list of worrying societal failure modes.
also the crusades were in significant part a competitive reaction to Islamic "proselytization via violence" so you're placing the blame on the wrong religion, there
I also don’t believe Christian societies are more honest than others. Every religion I know of teaches honesty, as does every non-religious ethical framework I can think of.
In Christian theory, everyone is a sinner, but in a real Christian society, people try to cover up their particular sins all the time, at least against other laypeople (not the priest), which leads to the opposite of honesty - hypocrisy.