One of Prozac’s side effect is alcohol intolerance. Aside from obvious mental effects of alcohol – Prozac & Alcohol can induce something called “Serotonin Syndrome”. “Serotonin syndrome” is not spontaneous drug reaction, it more like a consequence of excess serotonergic activity at central nervous system & peripheral serotonin receptors. This excess serotonin activity produces a specific spectrum of clinical findings which can range from barely perceptible up to fatal.
So in truth the chances of concomitanuse of Alcohol and Prozac causing adverse reactions are not very common, but it present!

Same things related to Zoloft and to Celexa which used for anxiety treatment. With MAOI class of drugs (like Nardil) – any alcohol consumption can lead to coma or to death.

So, advice of medical community is that what it is an avoidable & unnecessary risk.

Also on psychological note : Alcohol is depressant. It does not make sense to take (Antidepressant) Prozac and drink depressant.
Alcohol also has been positively linked to depressions. No one with any type of depressions or anxieties should consider drinking alcohol!

Take a note what better not consume any drugs with alcohol, in few cases it can lead to death of drinker. When effects can be small for person who drinking moderately, it can be deadly for heavy drinkers. Check my new article about alcoholism stages and what is moderate drinking and alcoholism.