Doesn Bayes Rule assume the predictors are independent?
Yes, strictly speaking it is only valid assuming the probabilitiy of e.g. “sex” occurring in an email is unrelated to the probability of “sexy” occurring in it. Obviously that is not the case. On the other hand, there is a long tradition of violating this requirement. When you do that it’s called a “naive Bayesian” algorithm and in practice it works pretty well, just as in practice (if you stay away from the edges of precision) it works pretty well to treat floating point numbers as if they were reals.
