If my household water is softened with...

It might. Softened household water can add salt to your soil. Over time, the salt can accumulate to levels that might be toxic to your plants. Household water softeners also remove calcium and magnesium from the water, and your plants need these nutrients for optimal growth. If you can, use your softened water just for your laundry and bath, having the softener hooked up to your hot-water supply only, and let the rest go untreated for your garden’s sake.