I think the answer to this is the same as Suzi’s answer to your question about why ice was clear but snow was white – kind of! When you see soap lather, what you are seeing is a bubble or a film of soap, which is very thin – far too thin to be able to show the dye or other colour which makes the soap have a colour. The impression that lather is white comes, I think, from the reflection of light off the surfaces of the components of the soap film. Does that help? Can anyone else contradict me?
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