If you are casting on a shared wifi, other people may be able to see what you are casting. They won't be able to see the video but they may be able to see the app/site name and the title of the video.
They may also be able to stop you stream and cast their own content.
You should look into getting a travel router. You attach that router to the public wifi, use it to make your own private network, and then link all your devices to that private network. That way, they can't see or cast to any of your devices and you are better protected from hackers.
