I have no idea what anhydrous magnesium sulfate is but I do know magnesium isn't a good additive to soap.
It helps create soap scum, reduces lather and at high enough amounts, prevents soap from forming properly.
ETA: Google tells me this is epsom salt? I know some people have used it in salt bars and it just doesn't work. I suppose a tiny bit would be ok but its not really needed.
Epson Salt is the common name of the heptahydrate (seven water) "version" of magnesium sulfate. I started with Epson Salt and baked off all the water. Anhydrous means without water. It makes a really good desiccant because it really loves water -- will pull it right out of the air and won't give it back unless you get it really hot.
OK. I won't put any in my soap. Thanks.
But it seems likely that it will accelerate the process of making gypsum.