How do I stop new stains from coming out of the washer?

I moved into a house in September of 2018. It very quickly became evident that new stains were getting on my clothes IN the wash, which is very very noticeable on dark loads. I tried a variety of detergents, premixing the detergent, adding a second rinse, etc. At wits end, when one spin issue then started, I... show more I moved into a house in September of 2018. It very quickly became evident that new stains were getting on my clothes IN the wash, which is very very noticeable on dark loads.
I tried a variety of detergents, premixing the detergent, adding a second rinse, etc. At wits end, when one spin issue then started, I ditched the machine and got a new. Did a dark load and the SAME issue.

After some online research, I got my water tested and it’s very hard with a lot of containment. The testing was done by a private company, so they were also trying to sell me a $9000 system.
I purchased Calgon water softener to add to each load, and thought it was helping the issue.
When the weather got cold the problem seemed to creep back. I avoided doing laundry here. It’s now in the 60’s here and I just did a dark load with Calgon and the staining worse than ever.

I am at absolute wits end. Does ANYONE have an experience like this they solved?

I am going to try calling the City Water Authority tomorrow, but this is from the same water supply as my last residence.
I asked a neighbor from one street over if they encountered anything like this and they have not

HELP
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