It's not necessary to demolish temples to get rid of the cultural penalty - upgrading them works just as well. Most cultural resistance comes from the governor's residence, not the temple, so I don't think it's worth bothering anyway.
The EB trait system is immensely complex; I am afraid that only the team knows how it works. I am pretty sure that temples have different effects depending on the faction and the primary personality traits of your characters. The one thing that doesn't matter is the "culture" of the temple. The trait-engine only looks at the building-line, so it can't discern between your temples of Zeus and those you conquered from other factions.
Most traits have small effects anyway: the idea is to create realistic "personalities", rather than characters dominated by a single trait. I would like to know what the "worshipper of" trait does, though. The description implies that there is a positive effect of being near the correct temple, but I am wondering if it's just a flag for other traits - to prevent the character from acquiring traits of other temple-lines.
Personally, I simply let role-playing decide the choice of temple. It's nearly impossible to predict the effect a temple will have on your characters; but it is likely to be small, and it will rarely be uniformly good or bad. The building bonuses are important, but won't win you the game. So role-playing the choice is more satisfying.
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