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."