Soaping Effect
It shows up most on emulsions built with certain emulsifiers, and on sunscreens, which tend to carry a lot of them. The first few passes look normal, then the film turns chalky and lathers faintly under the fingers, and a few seconds later it is gone. The name is literal: the emulsifier holding oil and water together is a surface-active material, and when enough water is present it does what surfactants do.
Three conditions make it worse — applying onto damp skin, working the product for a long time, and layering onto something that has not finished drying. Drier hands, lighter pressure and a pause between layers usually settle it, which makes this one of the few texture complaints with a reliable answer.
It is worth separating from two things it gets confused with. A white cast is mineral filter still visible after everything has dried down; soaping happens during application and leaves nothing behind. Pilling is small rolls of material lifting off the skin under friction, and those you can see and feel afterwards.
Formulators accept it because the emulsifier causing it is usually buying something else: a stable emulsion carrying a heavy load of oil or UV filter, or a lighter finish than the alternatives would give.
Nothing about it is unsafe, and the whitening is the emulsifier foaming rather than a sunscreen filter leaving the skin. It is a formulation compromise showing itself, not a defect.