Before the day of the festival, Carter will visit you and will ask you if you're gonna participate or not. It doesn't actually really matter whether you attend or not. If you chose to participate, Carter will give you an Ocarina to play with.
All of the bachelorettes except for Popuri will participate. Karen will sing a song, both Elli and Ann will play the flute and Mary will play the organ. Since you can see Carter, there's no way you can go inside the Confessional Room. It's also good to speak to the villagers before talking to Carter.
After the performance you will skip the day without saving your progress.