Hello: Actually it looks like we agree on softening, but not necessarily on the terminology. Softened water doesn’t directly affect the anode much, though it could cause greater localized self corrosion. This is where impurities in the anode itself create small galvanic cells. The main effect of softened water is as Randy says, greater water conductivity, which speeds up anode consumption so much that the anode can be completely used up in six months. I’ve seen this in the field and it’s impressive to this water heater nerd anyway 😎
I’d check for discoloration by running water from the drain valve. If there is any rust, that’s where you’ll see it first.