While we have frequently turned masculine English words into gender neutral ones, I cannot think of a single example where a feminine English language word has been made gender neutral. This would argue against calling the men in the coffee house "baristas" as well.
A similar sounding masculine word with the same root, "Barrister" comes to mind, but given that this word refers to trial lawyers in much of the English speaking world, and is used in that sense as a foreign affectation even in the United States, that seems confusing and inappropriate.
So, grammer gnomes, what is the answer?
Wikipedia takes the following stance (disagreeing with my statment above in some respects):
Since approximately 1990, the term barista (the Italian word for bartender - masculine or feminine; plural: baristi (masculine) or bariste (feminine)) has been used in English to denote a professional maker of espresso coffee beverages. Prior to that time, the less elegant prevailing term was "espresso puller." The shift of terminology probably comes, at least in part, from the fact that most espresso machines manufactured since the 1980s no longer require pulling down on a big handle.
Many makers of espresso machines offer barista training, most courses taking from one to three days.
A "barista" is the official title of a Starbucks employee who has passed training and a basic test.