My friend keeps reposting other people's posts from our chat to her stories, how do I ask her to stop?

I'd talk to her honestly, but gently - maybe she just doesn't realize that this is bothering you. Say something like: "Hey, I've noticed that you sometimes post our messages to your stories. It makes me uncomfortable because I don't always want all my acquaintances seeing what I say. Could you stop doing that?" The main thing is not to accuse her, just explain why you don't like it. People usually react fine if you tell them calmly.

If she starts doing it again, you can just stop sharing sensitive stuff with her or be careful about what you write to her. Honestly, after something like that happened to me, I started being more careful with some of my friends - if you see that someone might post your message, you just don't write them anything extra. You could also ask her to get permission before posting - that's fair and shouldn't be a problem for her if she respects you.

Or maybe she doesn't even notice what she's doing? Just send her a private message - not in the chat where everyone can see - something like "By the way, I'm more comfortable when our conversations stay between us. Could you not post them to your story?" No accusations, just like a fact about yourself. If she's a normal friend, she'll get it the first time. If she keeps doing it anyway - then there's a life hack: just stop posting interesting stuff in the group chat that she'd want to repost. Only post boring little things there, and send the actually important and funny stuff to her in DMs - she already knows she can only share that with your permission.

The main thing is to pick a moment when you're alone so she doesn't feel like she's being called out in front of everyone! In situations like this I always prefer to have a calm conversation one-on-one first, without witnesses - people take feedback so much better when there's no audience around.