This weird problem has been around awhile, along with mysterious little holes in cotton shirts. I think we decided it was probably not just one cause, but probably any number of things. Sunscreen, as you mentioned. Maybe moisturizers, chemicals on car seats, or even chemicals or oils left in the cloth from the processing and manufacturing. Some spots appear before the clothes were ever worn!

If you figure it out please let everyone here know. We will appreciate it.

I was getting some yellow-orangish spots on clothes that I figured out was from whatever it is that they use to "glue" on the "felt" strips on the dryer drum. I have since stopped using a real hot setting on the dryer (it's a gas dryer) and the spots have stopped. Are your spots on things that you have run through the dryer?

Yellow spotting on whites can be a phenomenon of using chlorine bleach. It's pretty well documented from what I can google. Did you by chance maybe use it in the wash water? I know I have bleached canvas sneakers in the wash machine and came out with yellow polka dots on otherwise just muddy shoes.

You might also have hard water which is heavy in iron. Too much iron and/or calcium might also cause yellowish or reddish spots on laundry.