What I'd expect from a Chaotic Good Theocracy.
Tolerance of other religions. As long as they aren't hurting anybody or being particularly offensive or ostentatious with their beliefs, other belief systems are at least somewhat accepted. More tolerance is shown to religions closer to their own alignments and beliefs, and lawful and evil faiths are generally accepted as long as they aren't harassing or harming anybody. Don't expect to get anywhere politically or culturally if you're part of those faiths though, and expect a few funny looks and plenty of gossip about your strange ways. Occasional bursts of intolerance from more hotheaded members of the community may rarely lead to public confrontations or vandalism though.
Small government. Possibly independent city-states each with a body of religious leaders who act as an advisory/judicial role to a nominal leader chosen by that body (possibly an official of the faith, or at least known to be a worshipper) who is wise and skilled. The town/city is the basic unit of government, at most the cities might form some league or loose confederation for mutual defense and trade, but that's about it.
Informal Laws. The laws are derived from the tenets or principles of their faith, with a heavy body of unwritten tradition and precedent. If they have inherited a sizable code of laws from their history, it's largely overlooked except for a few scholars and it only rarely becomes relevant. Minor violations, especially well meaning ones, are often overlooked. Outsiders may easily run afoul of the law out of ignorance, which is not an excuse if the magistrate is in a mood to make trouble for the offenders. Sentences are likely strict but relatively fair. Trials are likely quick and relatively informal, without a lot of tolerance for legal trickery or technicalities.
Small populations. Chaotic governments really don't work well for very large populations, I'd imagine most of the basic towns to be fairly small. The small-town everybody knows everybody effect is definitely in play here. There is likely only one temple/church of the dominant faith, with much of social life built directly around it. Besides the ruling priesthood, any other clergy (or those who derive divine spells from that faith) like Druids or Rangers are probably quite influential socially. There is probably a attitude that their religion "just makes sense" and they can't see why anybody would worship anything else, and likely have little understanding of other faiths outside of broad stereotypes.
Essentially, a league of small settlements of like-minded folks generally holding to a CG religion and alignment who live that way, expect everybody else (who's thinking right) to do so, and is willing to generally "live and let live" unless somebody makes trouble.
