Alginate doesn't stick to your skin or hair. It can be a challenge to get a LOT of hairs out of a mass of alginate, but it doesn't technically "stick". (Gypsum cements stick like THUNDER to hair, so be sure to use a petroleum jelly on any areas where gypsum might come in contact with the skin of hair.)
Alginate and stone will stick to your clothes however. While we're hoping you wore some old "paint clothes" or a good smock, it still happens and I'm going to tell you how to get it out.
We need a solution that has a high pH- alkaline. This will soften the alginate and/or gypsum cement and make it possible to brush off the clothes.
The most readily available way to get this solution is to dissolve baking soda in water. Use about 1/2 cup per gallon of warm water. Soak the item of clothing for about 1 hour. Take it out of the water and use a stiff brush to clean it off the surface. Wash in the sink or washing machine as soon as possible after that.
This technique might have to be done twice if the stain is really big, but it does work. Obviously the best way is to avoid it in the first place, but mistakes DO happen.