I was taught to cook red potatoes in their skins and peel them when cooked for potato salad. Is this an absolute rule and if so, why?

Boiling the potatoes in their skins theoretically reduces sogginess - they don't soak up as much water. I'm not sure how true it is, though.

While I agree that the skin on ANY potato tastes good, it is more common to leave the skin on thin skinned potatoes like red potatoes than a thicker russet. Having said that, if you are going to take the skin off a thin skinned potato, it will peel off very easily and take just the peel if you do so after it is cooked (as opposed to using a peeler and getting a fair amount of potato with the skin). Instead of using a peeler, just cut a slit in the skin and peel it off by pulling (like peeling an orange).

As long as the potato skin (any color) is thin, I do not peel. Tastes good to me.