Okay. Thinking out loud over here. Had a discussion with a friend the other day about principles. We have a common friend who is on some spectrum and kinda...impulsive at times. As in, making shitty/mean jokes or comments that, if this common friend would stop and think about it, would realize are at a minimum rude and at worst sexist. My friend is very principled in her action, in that she has a strict set of morals that she abides by at all times. She thinks any kind of objectifying behaviour is uncalled for and hurtful. And she does not want to be around people who she considers hurtful or toxic. And if someone acts sexist or misogynistic, this means that they probably are one or at least hold those kinds of ideas. When you combine the three, it means that she therefore does not want to be around anyone who has acted sexist / misogynistic / objectifying. Which I think is perfectly reasonable. But because she is quite strict in her moral compass, and has difficulty trusting people, she has a very low tolerance for any behaviour that doesn't jive with her principles, and she takes her principles quite far in my opinion (e.g. feeling hurt whenever someone whistles at her or looks at her with prying eyes). So in practice, and exaggerating for dramatic effect, it means she's hurt by every impulsive comment our common friend says, ergo cannot be in the same room together because she doesn't want to be around toxic people. Which has led to us deciding to break up a group so that she is no longer in the same time/place as our common friend, even though it is impulsive behaviour that in my opinion just needs time to improve. She also mentioned to me that she felt offended by a joke I made, which was basically a "that's what she said" joke about someone else's poor phrasing. And she said that it made her worry whether I might be someone to chuck in the bad-person-avoid-them-forever-bucket. (Despite us having a 2+ hour discussion of gender roles in modern society just a few days earlier.) And that puts me on edge? Because it sounds to me like such a hard line to draw in the sand, in an "you're either with us or against us" kind of way. I know enough people with far, far less favorable views of women that I don't want to be grouped with. And such a hardline position doesn't jive with my pragmatism, which puts "let's play some fun games with a large group" over "you want to avoid the occasional dick joke". On the one hand I get where she's coming from. But on the other hand I feel like her trust in me not being a bad person is razor-thin and easily bruised. I feel like I am one bad pun away from being tarred, feathered and outcast, despite her knowing me and my views for quite some while now. So I kinda think that that is her problem, not mine. But maybe I'm wrong, I dunno.
Don't divide the group to accommodate her. Invite everyone you want to invite. If she decides she doesn't want to go based on who'll be there, that's on her. It's unfair to your other friends to exclude them at her whim. You decide who you want to invite to your parties, end of story. You don't have to justify it to judge, jury, special snow- or bro-flakes. Whatever the reasons are, so long as they sit right in your heart, you're good. She's trying to snowflake you into inviting whoever she wants to your party. Fuck that shit. It's your party. Cry if you want to. But don't exclude your friend cuz she wants you to. end of story.
Your friend is ostracizing herself from you. Let her. Don't for a minute think that this has anything to do with principles. My wife has principles. She never cusses. Her moral compass is bright white neon. There are things that are right and there are things that are wrong. She is Lawful Good. I, on the other hand, are an ends-justify-the-means kinda guy. Everything has context. True story: if your car is registered to "X or Y" and you get a red light camera ticket, it comes to "X or Y." Then you have to sign an affidavit insisting you weren't driving the car. Which means either X OR Y can sign that affidavit and you weren't both driving, duh. So I sign my wife's red light tickets. Nope, totally wasn't driving. My wife signs mine. But my wife won't sign her own. She can't tell a lie, even to a robot in Texas that exists to rip you off. yet we get along, and rather well, and she loves hanging out with me, and she doesn't expect me to abide by her moral code. She's happy that I understand it, that I accommodate it, and that I don't require her to step out of her boundaries. But she won't forgive her sister who lied to her seven years ago. That's what a principled argument looks like. It's about your internal standards being assailed. It's about this person offended YOU not "they said something offensive." This whole walking-on-eggshells thing is because she's insisting that the outside world conform to her standards. She's not accepting of the world as it is and abiding by her internal compass, she's demanding that the world bends to her will. And if you give her an inch, she'll take a mile. These are people that need to spend some time alone. Why? Because they're shitty friends. They're not meeting where you are, they're not accepting you for who you are, they're not judging you based on who you are, they're friends with their ideal of you. They're looking through you and seeing some hypothetical version of you on the other side of the event horizon and it has nuthin' fuckin' to do with you, man. And maybe it's not her fault. Who knows what sort of trauma she's reeling under. But she doesn't get to spill it on everyone. She needs to learn to live in a world that hasn't been Nerfed to make her happy because the only people she can bully into behaving the way she likes are the ones who know her well and the more she acts like that the fewer of those people there are gonna be.
I would call her up and say "you know what? You've known me a long time. You know who I am. You know how I think. I'm not going to guard my language around you. I shouldn't have to. You know my heart and you can either accept me as I am or move on because I can't be friends with someone who stands ready to think the worst of me."
You are responsible for your own behavior. It sounds perfectly reasonable that she wouldn't want to hang out with your mutual friend, but from what you've written, it sounds like you ought to be extended the benefit of the doubt. Of course, she can decide whatever she wants. It's worth considering that she might be going/working through something.
She sounds like a very toxic and manipulative person. That kind of behavior can eventually lead you to isolating yourself completely and then being manipulated by hit hurt feelings. Don’t split your friend group for her selfish and snobbish reasons, that would be a grave mistake. Better to loose one manipulative friend than abandon friends because they don’t meet someone so else’s elitist standard