Is it harmful to water my household...

Softened water could harm some plants if that’s all you use on them. It is most likely to do harm to any plant that really prefers a light or sandy soil. The sodium ions in softened water tends to cause the soil to become compacted, destroying its aeration and its ability to hold water. So, we would advice caution if you’re using softened water. Don’t use cold water to water your plants. The best temperature is room temperature!