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 are right, Naive Bayes requires that the features are conditionally independent. Conditionally here means, conditioned on the class (the dependent variable). And indeed, a new feature $C=A/B$ would probably be conditionally dependent on $A$ and $B$.
But to really prove conditional dependence you would have to show e.g.:
$$
\forall z \quad P(A, C| Z=z) = P(A| Z=z) \;P(C|Z=z)
$$
where $z$ is any of the possible classes that your dependent variable $Z$ can adopt. This is different from showing e.g. that you can derive A from B and C.
