Comment by onedognight

Here’s my solution: clicking four boxes that form the corners of a rectangle will flip them leaving the rest of the board unchanged. Using this move you can find sets of rectangle corners with more white than red and just click them. This will converge to a solution. If you can find a symmetric board where all rectangle corners have equal red and white then this method would fail. I haven’t found one yet.

EDIT: I found some positions where this technique cannot be directly applied.