C.B.
Yup - I had this happen last year and was sooo mad! After researching the daylights out of it, I discovered it was the iron in my water reacting to the Avobenzone in the sunscreen.
You can get it out by treating it with an iron-removing chemical (I used The Works bathroom cleaner) but you may have to do several treatments and test each piece of clothing beforehand because it is harsh. Also, DO NOT get any of the iron-removing chemical on anything stainless steel because it will leave rusty-looking splotches on it and I believe you are supposed to wear gloves.
We got a new watersoftener and it has helped, but I still find orange stains when I use my beloved Ocean Potion sunscreens, which all have Avobenzene in them. I haven't found another sunscreen I love yet that doesn't. :/
Easiest solution? Find a sunscreen without Avobenzene in it. A lot of them have it now though, so you'll be reading a lot of labels.