Trial By Riddle

You have been sentenced to one of the many islands where everyone either always lies or always tells the truth. Can you leave alive? 

Inspired by https://en.wikipedia.org/wiki/Knights_and_Knaves
Made with the incredible Bitsy game engine: https://www.bitsy.org/
This is a work of fiction. All resemblances to people living or dead is coincidental.

Update: Added .bitsy file for playing this on bitsybox.