I went back to visit my mother once and discovered that for convenience she had started regularly running her cast iron skillets in the dishwasher.
It certainly damaged the seasoning IMO, but not as much as you might expect.
Not that I would ever do that.
In theory, soap shouldn't be a problem. The non-stick coating is polymerized oil bonded to the metal. It's not soluble by soap.
But there are conflicting opinions.