I bought a house in NJ about 6 years ago as my primary residence with painted cedar shake siding. In my experience there are two kinds of cedar shake: the wide ones with grooves that come pre-primed from the factory for painting and the smaller natural rustic ones that are not intended to be painted. You can get either kind from building supply stores, although they may need to be special ordered. I spent the better part of the first summer I owned the house carefully removing loose paint, priming and painting the house by hand with a brush. Given the texture of the shake and the need to get paint up underneath, it is a lot work. I also replaced a few rotten shingles, there is a special tool needed to remove them. When the paint fails in the future, I am not going to repaint it again, I am going to rip all the siding off and put on vinyl siding (with foam underneath).
If you have the unpainted natural cedar shake, as it sounds like you do, I would not recommend painting it all. There are natural oils in cedar that make it resistant to rot and insects, but can also making painting it difficult.
If you are looking to experiment, there are products such as "Wet and Forget" designed to remove mold, moss, and mildew. I have used this successfully to remove mildew stains from my roof and may work to lighten the staining on the siding. You just spray it on, but it takes time to work. Additionally you could experiment with using oxygen bleach to lighten the color of the existing shingle, or you try to pre-weather the replacement shingles.
But overall I tend to agree with your friend that it would be best to re-side it.