When having a FaceTime call, you can blur your background by tapping yourself and then the profile icon in the top left corner.
Blur your background during a FaceTime call
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Isolate your voice when talking
Let others hear you better by opening Control Center while on a call.
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6 FaceTime Features for Video Calls and Screen Sharing
How to schedule FaceTime calls, blur background, share screen, watch videos together, and use voice isolation