How to share my screen on hbo max without it going black on my friends screen?

Hello Ivory5,

When you're sharing your screen, others won't be able to see content that requires a subscription, a free trial, or a purchase or rental to view. With SharePlay, you can watch video together, listen to music together, or work out together by sharing content through supported apps.

You can read more about sharing your screen in FaceTime here: Share your screen in FaceTime on your iPhone or iPad

Best Regards.