How can I blur an entire video using iMovie or similar?
I work with a company that makes a product called Wondershare Video Editor for mac.  It is what I personally use so i can only offer my solution by this software. Check the screenshot first:

In a word, you can make it by the mosaic function in this software. Now i will show you step by step (8 steps in total).


Step one, import the video file and drag and drop to the video
timeline
Step two, click the power tool button to open the editing window
Step three, choose Mosaic function
Step four, pick up "Apply Mosaic to the clip"
Step five, click "Add"
Step six, adjust the size of blur area you need, if you want to blur
the whole video, drag the rectangular to the border
Step seven, you can change the heavy of this blur by dragging the
percent button
Last step, click "OK"


Done! Check the preview video screenshot as follow:
Export it, you will get a blur video. I wish it's helpful for you.