Cordy: "Billy Blim makes people crazy."
Lilah: "Not all people. Just men. He brings out a primordial misogyny in them. Turns them into killers."
It's not that Billy's touch (or contact with his blood) injects misogyny into men, but brings out a primordial urge. (Not to say that all men actually have a primordial misogyny in them in reality.) It's already inside people and Billy's influence amplifies it until it becomes the individual's overriding characteristic. Isn't that similar to Buffy and Angel? Love for each other is already inside them, as is self-serving motives and even being insensitive to other people's suffering (we all have that inside us, sadly), but the influence of Twilight is amplifying specific characteristics to create a Buffy and Angel melange so that they'll be just dandy about the world dying so they can go create another world where they'll live as gods. Think about that--the callousness is necessary so that Buffy and Angel will abandon this world and move on to the next. Twilight's influence needs to amplify certain characteristics in Buffy and Angel that will ensure it's creation--it's actually very similar in some ways to sci-fi/fantasy stories where you have the demon/monster thing using it's influence so the human mother will protect it.
Lilah: "Billy's touch works differently on different men. Some lose their mind in an instant. Others - can take hours. - Gee, I sure hope Angel isn't starting to feel testy."
The outside influence also would affect people differently. So Angel might be a more extreme case than Buffy or each person might have different characteristics dialed up depending on who's more susceptible--Angel might be more prone to callousness (like how he cut himself off in AtS Season 2) because for Angel is a struggle to connect while for Buffy it's more natural (though increasingly becoming a struggle). This would explain why Buffy rejects Twilight and goes back to help her friends and save the world--her ability to care about people besides herself and Angel hasn't been obliterated.
Fred smiles and shakes her head: "That wasn't you."
Wes: "How can you know that? Something inside me was forced to the surface. Something primal, something..."
Fred: "Do you wanna kill me?"
Wes: "Oh, God, no."
Fred: "It wasn't something in you, Wesley. It was something that was done to you."
The influence is something inside a person that's forced to the surface, but it's not really you but something that's done to you. Personally, even if it were just an alcohol metaphor, I believe being under the influence makes you a very different person. Lowering a person's inhibitions makes you a very different person than you typically are, but what if on top of lowering inhibitions, aspects of your character were magnified and dulled arbitrarily?
Struggling to find a connection to others has been an important theme for Season 8 and Buffy's emotional character arc. She struggles to "feel it" even when she's just normal, old Buffy. Imagine how Buffy would act if the aspect of her character that disconnects suddenly became the dominant part of her personality.
So everyone who's saying that's not my Buffy or that's not recognizably Buffy--I think you're right. It's her, but it's not her at the same time.