N.G.
I think she will do better than you think she will if you just start leaving her as opposed to hanging around to make sure she is OK. I make it a point of not hanging around when I drop my daughters off somewhere, I think that makes anxiety worse, IMO, and have heard teachers and daycare workers say the same thing.
I used to manage a girl scout troop and no girl ever cared when her mother left, and some of them were VERY shy.
Also, again just in my opinion, giving into those anxieties by allowing her to stop activities just reinforces the behavior. She's only 6. My five-year-old makes declarations all the time about what she wants to do, but in the end, I know what's best for her. She told me she wanted to quit Taekwondo, but I know she doesn't, I know she's just bored with it right now (her instructor is changing some things). I told her to wait a few weeks and we'll see how she feels then.