yes, it's true that you can damage the plants because of the sodium from the water softening process.

Often it's only indoor water which is softened. So you may be able to use an outdoor spigot/hose.

That said, sometimes people put the entire system on the softener. So check how your system is set up.

Salt makes for unhappy houseplants.

Water softeners usually work by ion exchange in which the water is fed through a container of resin and sodium is released into the water reducing the hardness by replacing magnesium and calcium, which is absorbed into the resin.

There should be a by-pass faucet on your softener to get unaltered water.

Someone else may be able to explain it better but that's that general idea.

If you have a dehumidifier, it's an easy source of sodium-free water. And as dellis326 says, look at the pipes around your water softener: you'll probably be able to find a place to get water upstream of the softener.

When you water, do you water enough that some flows out the bottom? Any amount of sodium above minuscule isn't so great for plants, but if you water in sips you'll have a lot more of it accumulating in the soil.

Soft water will eventually destroy your garden, it happened to my father in laws garden after 4 to 5 years of watering with it. His tomato plants would die before they even got to set fruit, all kinds of pests and blights plagued everything. He got his soil tested and the said TOO HIGH SALT, too low magnesium and calcium. Which that is what a softener does, takes out good and puts in bad. He had heart attack years later too, another minor side effect of prolonged soft water abuse