Around here, whether it is legal or illegal to remove stones depends on the location. There are all sorts of state and municipal laws relating to whether it's public land or private land, and also whether you are picking the stones from below the average tide line. For example, a private beach is only private to the median tide line. Below that, it's state/federal land, and the determinant becomes whether it's a protected beach.

Yes, it's complicated!

The place on the Pacific coast that we like to go to is actually First Nations land. That has its own set of rules. In this case, we have permission from the tribal administration to pick up stones, primarily because I gifted one to the Tribal Elder who came along one time to ask what we were doing!