I would not use softner water.

Looks like sunscald. What zone are you in or what area of the country are you located? High temperatures during the day? While outside, have the leaves got wet due to rain followed by clearing skies and sun?

They will probably recover from this, but while hardening off, they need to be introduced to the sun gradually. Ideally, they go outside into partial shade / dappled sunlight and then over the course of a week or so, gradually position them to get more sun.

They need to be acclimated to the intensity of the sun. There are other possibilities but I would think sunscald of the leaves is most likely what you're seeing.

Second : Sunscald.
Probably you hastened in giving them direct sun in the process of hardening off. They should recuperate.

Seysonn

sunscald it is!

You are also seeing some interveinal chlorosis and it is in the older leaves. That is usually indicative of magnesium deficiency. When plants are deficient in Mg. It's possible your soft water and the salts it may contain have skewed the soil pH. That's a chronic problem I have to deal with here.

Switch to watering with un-softened water and if it continues I'd try watering them one time with a weak solution of epsom salts dissolved in water. Most soils don't require MG supplements but soil-less mixes can be deficient.

Dave