Water softeners work by replacing the calcium and magnesium in the water, often with sodium. Calcium and magnesium compounds are the components that make water hard, leading to lime deposits on plumbing and making it hard for soaps to develop a lather. They are important nutrients for plants though, and sodium is not. Softened water can also affect the soil structure for a potted plant, just as too much road salt can affect the soil structure of the nearby soil. The sodium compounds accumulate in the soil of the houseplant, and can cause problems for the plant.
Different plants have different sensitivities to sodium itself, but sodium can also affect the soil.
With a few simple remedies the problem can be solved. First, if there is a source of unsoftened water, use that water for your plants. Rainwater is a good source of water for this purpose. If you have a faucet in your water line before the water softener, you can also use that tap as the source of unsoftened water for your plants. If you have been using softened water, flush the soil with a good watering of unsoftened water, letting the unsoftened water rinse out the sodium from the soil medium.