I also think there is a huge between "not listening" to a child and letting them do whatever they want.
My son is 1y older than the OP's girl. Last year his school was doing a Christmas carol concert in the local abbey. At first he was up for it, but as it approached, he became increasingly nervous and started saying he didn't want to do it.
I did listen to him. I asked him about his feelings. I asked him if they were in his body, like butterflies in the tummy, or his mind. I asked what he thought his friends felt. I also talked about how I had felt nervous in the past, how it was normal and happened to everyone, and how it was just a feeling and not a sign he couldn't perform well.
But we didn't say he could just quit.
We told him, our family's values are trying our best and not giving up. That meant, he had to practise his little song once every day. On the day, he needed to put on his costume and walk with the other children without a fuss. When he was there, we had prewarned his teacher, and he could see if he felt he could be brave and get up with his friends, or if he couldn't, he had to be part of the team anyhow, by wishing his friends good luck, helping with any little jobs like handing out music sheets or stacking chairs, and then listening nicely to his friends and clapping for them.
If he made a fuss, there would be a consequence. If he just went and helped, no problem. If he went and performed, he would get a small prize like a sticker book that he wanted.
It was his choice.
He did it and was very proud of himself and told anyone who would listen how brave he had been. I really hope he always remembers it and how he got over his nerves.