My experience is the answer is yes. I have been using softened water for all of my indoor plants for years. I also use it for growing all of my pepper and tomato seedlings indoors.
My son did a science fair experiment comparing different types of water for watering different kinds of plants. Since at our house we have water direct from the well, RO water and softened water. We used tap water from a neighbors house also. In order the best growth was from RO, Softened, Tap, then well water. I have theories as to why.
If you google it you will find many answers saying otherwise with no scientific evidence. The EPA does consider softened water safe to drink and classifies it as āvery low sodiumā
There was a debate on social media years ago that i enjoyed reading up to a point⦠as it went way off the rails. Similar threads on reddit etc.
Rainwater/Snow etc was said to have more minerals and nitrates (nitrogen) as well as hyrdogen peroxide by some person and they āprovedā it was better vs tap water which had been chlorinated.
Also older decades old discussions on it.
It gets interesting in the winter time as these folks come out of the woodwork and tell how they grow things in snow water⦠etc etc.

The best discussions are āIs it SAFE to use rainwater or snow water for plantsāā¦

Many of the FB experts will say āNoā.
Purely anecdotal note, from my personal experience.
Iāve noticed that when I water my outdoor plants with hose water (a.k.a. tap water), they need to be watered far more often. When I water them with captured rain water, they are significantly more drought tolerant and grow much better. My suspicion is that this has to do with the presence of too much calcium in our water. (Thereās also way too much calcium in our soil.) From what Iāve read, too much calcium can make it hard for plants to absorb other minerals they need from the soil. So maybe thatās why?
But itās not a scientific experiment, because I donāt have a control group. There are plenty of other hypotheses, as well. For instance, my rain tanks also have dead bugs and autumn leaves that fall into them (I donāt bother to filter things out), so my plants may also prefer the rain water because there are bound to be beneficial microbes and nutrients in it.
I think this is the reason RO water performed the best in my sons science experiment. RO water will have similar tds to rain water.
I have also noticed that my garden seems to respond much better to rain than it does to watering from the well.
How do you apply the well water?
I have well water at my house. The water comes into my house and goes through the softener to supply all the fixtures inside the house and one fixture outside. There is a bypass before the softener that supplies 2 outside yard hydrants and one outside hose bib.
I water my outside plants with a hose from the yard hydrants.
I was wondering if the response of the plants may have something to do with how the water is distributed and how much.
I grew container nursery stock for years. We had about 80 acres and supplied water from creeks, wells, ponds, and we recaptured about 600,000 gallons a day and recycled it back on the plants.
So we would keep nutrients out of the environment and reapply it to the plants.
We also had high carbonates due to our limestone gravel pads, and our recharge wells were high in carbonates.
I always noticed a very positive response in the plants when we would get a large rain event, especially after long periods of no rain. Like several days of rain or 2"+ of rain in an event. Where we wouldnāt have to run irrigation for a few days afterwards.
It would take a few days to a week and tired plants would wake up and show more vigour and look happier⦠so to speak.
I always attributed it to fresh clean rain water either giving the plants a total watering as apposed to keeping them going through the summer with irrigation. I also always thought it helped flush salts and carbonates out if the pots.
Some say it also carries some nitrogen in it. Iām not sure, but Iāve heard that suggested before by my peers. I would like to believe it.
There is something special about rain water.
Tap and well water is just going to depend on the local quality of the water. RO should be good and Iāve never experienced issues with soften water. Usally the by pass hydrants are there to eliminate the cost of softening large quantites of water for outdoors use.
I would make the general blanket statement that, yes, softened water is safe for houseplants. I do want to add a caveat, though. There are some plants that have a salt sensitivity like ferns, many palms, African violets and calathea.
With the additional salt thatās being added to the water supply, it would be prudent to stay away from the chemical fertilizers and use something like liquid seaweed or fish emulsion for those with salt sensitivities. If you currently grow some of the āsesnsitivesā and they arenāt showing any signs of salt damage, then theyāre probably fine with the current salt levels and care regiment and thereās no need to worry.
(Common symptoms of salt damage are brown leaf edges or tips, chlorosis (yellowed leaves) and stunted growth.)