Red Cliff Campground 

Heads up: Work crew at present roadwork below campground says Red Cliff ("the whole area") is closed by FS until July 1st. Confirming with FS presently.

I'm pretty sure that this cliff is limestone that has been stained.

It very well could be. The only limestone I have climbed has tended to be a darker gray color. I suppose I have seen some that is more of a tan as well. I read somewehre else that this was sandstone, and looking at the rock it was very red. However, the ground there was saturated with what looked like red clay. So as you point out I suppose this could be limestone stained by the red clay.

The rock formation did have a lot of pockets typical of limestone, so it is very possible.

FWIW, there is a such thing as red limestone. Iron oxide in surrounding soils can turn the limestone red, yellow, or brown, whereas carbon impurities will turn it the typical blue, gray, and black. Often combination of these minerals streak or stripe the exposed cliff creating the "black & tan" and blue & gold combination that are so appealing. Think Black & Tan cliff outside St George, Utah or the French Cattle Ranch at Tensleep, Wyoming or even the walls of areas like Ceuse, France or limestone crags in Spain. Red & brown limestone is not unusual to find in areas such as Montana and Wyoming.