It's possible but locals and I imagine most tourists actually buy sunscreen in Hawaii and it's only legal to sell reef safe sunscreen there.
https://www.hawaii-guide.com/blog/hawaii-new-reef-safe-sunsc...
https://www.hawaii-guide.com/blog/hawaii-new-reef-safe-sunsc...
Many of the dive boats and hotels will offer sunscreen out of a bulk pump, so depending on what you do on the islands, you probably don't need much on your own - just a small tube for your group will do.
Point is, the regulations to keep those ingredients out of the reefs have been mostly successful.