It's always difficult when you are in love with someone to have your perception of them shattered. You love your girlfriend, and you don't want to do this, but it's been made clear, without say as much, that this is a deal breaker in your relationship.
If I were younger, I would tell you that "She can't stop doing it" is not true. That she's being selfish and prioritizing her desire for an open door policy over her commitment to you. That, this is one of those cases where it's not "you would if you loved me," but, "you wouldn't if you loved me." But, I'm not younger. I don't see the world as black and white as I used to. There are people who are perfectly capable of great love, but NOT sexual fidelity.
Recently, Dan Savage, who writes the advice column "Savage Love" covered the topic (look up "Savage Love", and "Sex Before Dawn") Where people thanked him, saying that they thought there was something wrong with them because they were capable of great love, but could not keep from stepping out on their partners. One woman said she loves her husband, but sex with others is like a safety valve for her that helps her maintain her sanity. Dan's strongest advice to people in this position was, 1) Accept that you are one of those people that can love, but cannot remain sexually faithful, and 2) Be honest with your partners. He suggested it's best to seek partners who can accept this.
On the surface, it may seem that your girlfriend is being selfish. Telling you that she wants a man but will settle for a woman as long as you don't touch her seems to reinforce this. But, you would be amazed by the one-sided rules that many swingers have, and this doesn't even come across as the worst I've heard. So, maybe it's not about selfishness. Maybe she has simply expressed that she is not a monogamous person, that this is something she enjoys, and she wants YOU to enjoy it with her, but she's not going to change who she is and suddenly become completely sexually faithful, even if she loves you.
The question is, can you handle it? You're here because you don't want to lose her. But, you don't want to do it either. And, from a swinger point of view, that's a deal breaker. One partner says no, it's no for both. The relationship is more important than the extracurricular play.
But, sometimes it's not that simple. Sometimes, even if we choose not to believe it, there are people who simply are not cut out for fidelity, even if they are capable of great love. And for them, there are people who either work the same way, or are very open and very accepting and can give them that freedom. You have to figure out if you are one of those people, or if you need to move on and find someone who can love only you, and wants to love only you.
One bit of devils advocacy... if 50-60% of all men and woman are unfaithful to their partner at some point in time in their relationship, the odds are against most of us. As tough a pill as it is to swallow, would you rather have a partner who is open about her need for non-monogamy? Or, one who, for whatever reason, years down the road, commits an indelible act that they can never take back and you can, possibly, never forgive?
One is the devil you know, the other is a matter of faith and trust. But, that's what relationships are supposed to be built on anyway.
Good luck! I hope you find what you need.