Incoming phone calls, whether you answer them or not, will take over your entire iPhone's screen — no matter what you're in the middle of doing at the moment, including live broadcasting. Unfortunately, Apple does not allow app developers to interfere in any way with incoming or outgoing calls. However, there are steps you can take to avoid getting interrupted by a phone call.
Enable "Do no disturb"
- Go into your phone's "Settings" and click into the "Do Not Disturb" settings
- Make sure "Silence" is set to "Always"
- "Allow Calls From" is set to "No One"
- "Repeated Calls" is set to "Off"
Now, whenever you put your phone into "Do Not Disturb" mode, all of your incoming phone calls will go straight to voicemail and your stream will be uninterrupted.
To put your phone into "Do Not Disturb" mode, simply swipe up from the bottom of your device and tap the moon icon.