Calcium sulphate is what I have plenty.
Calcium sulphate (CaSO4.nH2O) is also known as gypsum or plaster of Paris. It's slightly soluble in cold water (~ 3 g/l) and almost insoluble in hot water. Calcium chloride (CaCl2) is much more soluble (~ 800 g/l).
So if you need more than about 2 g/l of calcium chloride, the replacement won't work as you just can't dissolve enough of the sulphate. Also, any lumps of calcium sulphate risk solidifying in a fairly short time, depending on which form you planned on using: plaster (hemihydrate, solidifies when wetted) or ground gypsum (dihydrate).
(That's of course assuming you can get food grade calcium sulphate, technical grades are not necessarily safe for food use)