If I engineer a new feature such that feature C = feature A/feature B, must I drop features A and B from a Gaussian Naive Bayes model? As the question asks, is it bad data science not to drop the dividend and divisor features when creating a new feature that is their quotient when working with a Naive Bayes model? My understanding of Naive Bayes is that it assumes conditional independence of the variables. In my example, feature C would not be conditionally independent of features A and B if, knowing C and B, I could derive A; or if, knowing C & A, I could derive B.
Is this correct?

You don't have to.
It's true that Naive Bayesian assumes the features are independent conditioned on the class label. But it's OK to make wrong assumptions, because any model is just a set of assumptions after all, one can't be sure if all of the assumptions fits the reality.
So, as long as adding the feature results in a better model selection criteria, such as BIC, then you should do it.
As it said "all models are wrong, some are useful"
