The issue here is whether an atheist needs to study all religions in order to be an atheist. The barmaid seems to concede that point since she advances arguments that require knowledge of specific religions. Both of her examples require the provisional acceptance of gods because they refer to particular properties of those gods (i.e. whether they can have sons and prophets).
A Christian, for example, would happily engage the barmaid in a debate about the the divinity of Jesus as long as they begin with the assumption that gods exist. In order to engage seriously in that debate, the barmaid would have to read a ton of Christian apologetic literature. In other words, she would have to understand "sophisticated" religion. She would not be defending atheism even if she won the debate since there are billions of religious people who don't believe in the divinity of Jesus.
how many angels can dance on the head of a pin.1
The atheist barmaid made a mistake. She should have said "Let's see - I understand that all religions begin with the idea that gods exist. What evidence do you have that this is true?"
Or, for that matter, the problem of evil. If there are no gods then there's no problem. Debating the "problem" of evil or whether Jesus is the son of gods is just like debating the cut of the Emperor's new clothes [On the Existence of God and the Courtier's Reply].