This is a tricky one.
As for the selfish part... I don't believe there are any truly altruistic acts. Even the most kind and considerate action makes us feel good about being so kind and seeing the other person happy.
I think it's actually fair that you're considering the impact of him breaking up with her. You're just being realistic.
In terms of your discomfort with his girlfriend's personality and the way that she chooses to conduct herself... that's incredibly difficult.
Some people take the perspective that it's their partner's business and they don't have to even like this other person.
Other believe that it has a greater effect on the relationship between the original two people.
I'm not sure there is a right or wrong here. I think it comes down to your own personal expectations and boundaries.
If you don't like the girl, think she's bad for him and don't want her sleeping in your bed, I can understand that.
That being said, if you are of the viewpoint that he can choose to date whomever he wants, you have to be careful about putting restrictions on him that could make that concept difficult in practice.
I personally wouldn't want my girlfriend to date someone who was cheating on someone. I have a strict moral limit about it. I absolutely hate cheating. My girlfriend, on the other hand, thinks that there are two sides to every story and that if some people are 'stuck' and 'repressed' in their relationship, they have a right to happiness. She thinks that many monogamous people are selfish for not being open to poly. I don't agree with her, but there we go. She has a long-term online/phone lover whose wife doesn't know about it and she would sleep with him in person if she could. I find that difficult, but leave her to it and try not to judge, as he does actually seem good for her. Not toxic, like your husband's girlfriend. So I bite my tongue and let her get on with it.
Toxic partners can cause problems for everyone. Some people can turn a blind eye and some can't.
My girlfriend hated one of my other girlfriends. This girl lied, cheated and was quite toxic. I was completely enthralled with her. Your husband probably feels the way that I felt - toxic people push and pull you, create all kinds of emotions in yourself and they become like a drug. They can make the sanest of people fall apart and the most sensible of people crave them.
After about 8 months of seeing this other girl, my girlfriend became increasingly uncomfortable whenever I talked about her or spent time with her. In the end, she told me that if I kept seeing this girl, it would probably lead to the end of our relationship. That was her limit.
I've never known if that was right or wrong. I've resented it at times and understood it other times.
Can you cope with him being with her? Can you cope with the drama she brings? Would it ever end up being a deal breaker for you?
Perhaps you need to think about those things in your own mind and then think about what kind of restrictions would be fair. A more casual arrangement *could* work. But casual tends to end up drifting back into what it was.
Incidentally, what reasons did she give for lying to him about seeing this other guy? Or are they really irrelevant?
me: female, 28
GF: my girlfriend, female, 38
Hubby: my metamour, her husband, 34
2 year, open poly V relationship, LDR