Big 5 is not an established scientific theory, it has never been. In fact in the field of psychology, personality is as useful as a concept as your astrological sign is. There is no evidence that personality trades exists outside of factor analyzing pen and paper tests, let alone that they can be measured and classified.
For personality to be a useful psychological concept it would need to be predictive of behavior. So far we have more evidence that religion has a bigger role then personality traits. E.g. studies find that the more religious people are the less they obey in the Milgram experiment, however there is no evidence that people that score highly on the agreeableness factor do.
I went and did some exploring of the literature and found a study[1] that seems to contradict this statement. E.g. they found a significant correlation between Agreeableness factor and obedience in the Milgram experiment. However, the effect size is fairly small. Political leaning was also significant with similar effect size, and this study has yet to be replicated.