I have well water and a softener.
So do millions of others.
For most healthy people, the amount of added sodium in the softened water poses no health problems.
However, for people who are hypertensive (have high blood pressure) and must live on a low-sodium diet or a sodium-restricted diet, the sodium in the softened water can be hazardous to people's health.
I have never had a chicken or chick suffer from the low levels of added sodium.
Also, if you are still concerned, if you have a well, you probably have a pressurized storage tank.
Most are plumbed with a spigot near the bottom for flushing any accumulated contaminates.
Put a hose on it...
I did some more research and found this opinion/fact:
2. Well Water
About 15 percent of the U.S. relies on private wells, which aren’t regulated like municipal water sources. Wells can be polluted by natural and man-made contaminants, including microorganisms, like bacteria and viruses, heavy metals, and unsafe levels of naturally occurring fluoride. Chemicals or animal-waste runoff from farms can also contaminate wells, especially if they’re shallow.
If you have well water, test it for safety. If you drink it yourself, consider it safe for your livestock, too. But, if you
don’t drink your well water for reasons like heavy metal contamination, chemical pollutants or microorganisms, remember you are what you eat—and you are what your food eats, too. If you eat the eggs or meat of your chickens, don’t give them water you wouldn’t drink yourself.
3. Softened Water
Water softeners commonly use salt (sodium chloride)—the same stuff in your kitchen saltshaker—to replace the calcium and magnesium ions that make water hard. Hard water’s biggest caveat is scale buildup. It’s not unsafe to drink, but it can clog pipes, build up around faucets, and keep your soap from lathering in the shower. Water softeners installed where water enters the home can protect pipes, making the naturally hard water unavailable.
While water softeners use common table salt, the process of softening is only replacing calcium and magnesium ions with higher-charged sodium ones. Very little sodium ends up in the drinking water. Even for people on a sodium-restricted diet, the FDA says that the amount of sodium in an 8-ounce glass of water is so low that it still falls under its own definition of a very low-sodium food.
Consider that if you’re giving your chickens any kind of electrolyte products, that it contains more sodium than they will consume from softened water. Sodium is an essential electrolyte. If you’re sodium sensitive and use a water purification system that uses potassium chloride in lieu of sodium chloride, this is also safe for you and for your flock.