Blur screen live on macOS
Not exactly blurring but you can use the following app to create a floating "snap" that can be used to conceal part of screen.

Snappy - Snapshots, the smart way is a free app that you can download from the Mac App Store.

Snappy lets take create snapshot of a part of screen or entire window which remains floating on top of all other windows. You can use it to create a blank snapshot, (such as one of blank portion of screen or part of wallpaper). This snap can be moved around or freely resized. It is possible to adjust the alpha value for the snap using the context menu. It doesn't actually create a blurred view but you may find that useful.

Also, it takes a simple mouse click to get rid of the snap. Snappy app runs in Menu bar, and keeps track of all the previously captured snaps (which can be re-invoked using a simple click).

A sample is as shown below:



Here I have created a snap of the white portion of the browser viewport and resized it to conceal the part showing the question.



Note: No affiliation whatsoever to the developer.I find this app super useful in my workflow, where I need to keep around snap of some part of the screen.