People take baths in it so it clearly doesn't. But if epsom salt is the salt of sulfuric acid when it dissolves the chemical ions present in sulfuric acid should also be present in the bath water and in abundance enough to melt you.. right?
I also remember that water autodissociates into hydronium and hydroxide, so my other question is why wouldn't plain water simultaneously be a acid and a base and also just melt you?
If there's a trillion (or whatever) water molecules next to your skin and even a tiny fraction of them turn into an acid and some of them turn into a base, there'd cumulatively be a lot of acid on your skin. I can't imagine adding salt which would also ionize could help things.