How do I blur the background, but not a moving subject in FCPX to create a depth-of-field effect?
FCPX can't do this automatically (like Photo Booth) unless the background is a single colour.

As a workaround, if possible…


Take a picture of the background.
Film the vlog in front of a green screen.
Key the background leaving the alpha channel.
Place the picture behind the video layer.


There is a full guide in this Apple KB article:


Final Cut Pro X: Use chroma keys