Do you have a tub or front-loader? Does it happen with every wash? Does it occur in the wash or rinse cycle (try without using detergent).

You seem to have controlled most variables. Now for the water source for which you will need to consult a pro. You might try filling your washer ( tub washer, small load) with water from a source that does not flow through the same pipes.

I had this happen in one apartment we lived in the landlord told me it was "gravity". I didn't know whether to laugh or cry. We never got to the bottom of it. I'll be following this thread to find out what it is. I wish you luck. It is infuriating for sure.

I found this in houzz. Maybe it will help. https://www.houzz.com/discussions/2429527/weird-spots-showing-up-on-my-cotton-t-shirts-after-washing-help

Hmm ok thanks for the link. It seems like many people have this usury but they never found a solution. What could it be????

Water heater could be old and disintegrating. Have you checked its age?

I had that happened to me once or twice when I used the ”normal wash” on my machine with a large load and liquid detergent. Probably too much of it. Maybe I used softener as well, I don't remember. My machine uses very little water in normal and the stains were undisolved product. I now use other cycles and pay attention when I have full loads to use appropriate cycles. I dont use sofetner either. I never had stains appear after those changes. What kind of machine to you have and which cycles do you use? What happens to the stains after you wash the clothes again? If they are easily removed then I doubt they are oil.

Food and grease stains not coming out...... try pre-treating food stains.....wash in hot water to remove oils