How have you treated them to date? Has a wax product been used on them (by you or the installer)?

Hard water in your locale?

They are efflorescence stains.

Here is a link that might be useful: efflorescence

I have my doubts about efflorescence from soapstone. Steatite (the predominant mineral in soapstone) is totally non-porous. Of course, there may be other components to this slab, some of which conceivably could be porous and efflorescing, but I sort of doubt it.

You cannot hurt the soapstone with the treatments I will suggest. I would try, in this order:
-nail-polish remover (acetone) or, better, mineral spirits. This would test my theory that it is a waxy deposit.
-CLR or Lime-a-Way. This would test hollyspring's theory that they are hard-water deposits.
-Nitric acid or muriatic acid. This would test barthelemy's theory that it is efflorescence. (Some efflorescent salts would be removed by CLR, too.)

Any update on this issue with soapstone? we are considering soapstone for our kitchen countertops and our fabricator is strongly encouraging us away from it. He had one of his clients send us picture of her soapstone that looks very similar to above (although a lot more of the "bloom"/crystallization looks like it occurs around the white veins). She said it was fine for about 1 year, then started these white spots. She had the countertop resurfaced and still not taken out. So she had the countertops replaced with something else.