I'm going straight for the kill.
Remove Him From The Group
There doesn't seem to be any other applicable answer. The biggest red flag here is that he has already been talked to and ignored the feelings of the rest of the party. This is a major no-no in RPing, at least in my groups. Ignoring the next portion of my answer, this alone is the main reason they should be removed. They were asked to stop, in-character and out, and they didn't. They came up with an answer about how their style is more important than the comfort of everyone else. Get him out, now, and send his character to the barber for a head shortening.
If you don't remove him you risk alienating yourself or the other players, likely causing them to either quit or go elsewhere.
I wanted to explain in further detail my answer, but this is strictly opinion and not necessarily coming from my experience as a GM. It seems to me that the player is living a power fantasy through his character, and this sort of behavior is never something you want at your party. Writing off his behavior1 as "that's how my character would act" is the standard excuse of people who either wish to be offensive for the sake of offense, and/or genuinely don't understand why such issues might be a problem and suffer from a glaring lack of inter-personal skills. This sort of behavior and ideology can only serve to drive the player's fantasy while alienating the others at the table. In short, this is extremely sexist behavior. If you really want to give him another chance, you need to explain it as such and suggest ways to let his character have the air he desires while making it comfortable for everyone else.
Second, saying his character would be rude and a rapist because he's a barbarian is a logical fallacy. If we're staying in the fantasy format, what makes a barbarian a barbarian is typically an adherence to combat as a "fun" activity, along with typically wearing few clothes usually made of cloth or leather and having a big stick to hit things with. Being "rude" usually comes from hailing from a foreign land and not understanding local customs (like the westerners when they first came to Japan), having different social hygiene standards, or doing things in a manner that doesn't follow the "refined" ideas of society. A barbarian who is rude in a country where they know the social standards isn't rude because they're a barbarian, they're rude because they're just rude.
Additionally, though the excuse that rape has always tinted our history has always been an argument used by people who support those power fantasies, there's little evidence that I've been able to find2 that suggested there was more rape then than there was now. Usually their idea that rape occurred more is based on Hollywood more than actual history, such as claiming a certain Mel Gibson movie is historically inaccurate and it had a lord raping a woman.
Essentially, saying that his character participates in rape and being rude because he's a barbarian is a flimsy excuse at best.
Building A Better Barbarian
I can't leave off without offering a way for the player to make a barbarian that might be more welcome to the party. This character idea can easily fit in the place of the current one, and doesn't have to be stuck to its "evil" chains that it was initially displayed as.
I submit, for your approval, Shan Yu from Mulan.
Shan Yu, in my opinion, is the perfect example of the evil barbarian. Brute strength, intelligence, leadership, Shan Yu had it all. He knew how to work with a team and inspire people to follow him without having to use fear. Granted, in the movie he and his group are Disney-level evil, but he could be excellent inspiration for a good barbarian who wants to remain "bad-a*#" and still play in a way that makes others feel comfortable and welcome.
1: And this is his behavior, going by his answer when asked to stop and given the reason why.
2: Admittedly, I'm not a scholar of such things.