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Say
1. I want to change the area in white to red (the action)
2. *except* the selected square
I know how to do 1. with "By color select", but not 1. and 2. combined. Could someone make a suggestion?

More generally, how can I exclude a selection from an action?

Quote:...More generally, how can I exclude a selection from an action?..

Once you have the background selected and switch to the rectangular select tool.

Change the tool 'mode' (in tool options) to subtract, draw in the rectangle, hit the enter key.

[attachment=4595]

However, making the initial selection can effect the outcome, selecting the white, will give a border of semi-white pixels.
Various options, shrink the selection by a pixel or two or in this particular case select the black circle and invert the selection.
 
30 second example https://i.imgur.com/wXVatrA.mp4