Effect of outliers on Naive Bayes
There are different flavors of Naive Bayes, so the answer depends a bit on the use case. 

One potential issue with outliers is that unseen observations can lead to 0 probabilities. For example, Bernoulli Naive Bayes applied to word features will always produce 0 probabilities when it encounters a word that wasn't seen in the training data. Outliers in this sense can be a problem. However, all these and similar issues of Naive Bayes have well-known solutions (like Laplace smoothing, i.e. adding an artificial count for every word) and are routinely implemented. 

In Gaussian Naive Bayes, outliers will affect the shape of the Gaussian distribution and have the usual effects on the mean etc. 

So depending on your use case, it still makes sense to remove outliers.