I'm thinking of watching a movie with gay characters with an 11-year-old I babysit without asking her parents
Are you sure about this? Are you sure their parent's won't mind?
I don't think the movie is going to be very good.
You are responsible for the child's well being because they trusted you. You should be a proper baby sitter or lose your job because you can't behave properly and ask things ahead of time.
I'm going to watch it, who doesn't like movies about gay characters.
Some parent's may not like this type of content being shown to their children. You should always talk to a parent's child and get their permission before showing them something that they may not approve of. This way you won't have to worry about being fired if they find out later on.