I guess I'll have to agree to disagree. I bring toys to the beach for my kids to play with, not for anyone who might be there for the day (and yes I used to share, but then my kids' toys would be unavailable for them to use when they want to, which is not something that is easily predictable for a two yo, or in some cases we have had toys returned to us broken with not so much as a sorry, or we have even had toys just left on the beach for the tide to take them away and never be returned to us as those who borrowed them had already left the beach)
DH asked me what are we teaching our kids if they feel entitled to use any toy on the beach that they want, even if they don't belong to them. Would I as an adult go up to a complete stranger and say "hey, that's a really cool beach chair, can I borrow it?" or "hey that sandwich looks divine, mind if I have some?" I'm not trying to be stingy, really, but I am trying to remember that I am raising children to someday be adults, not to be perpetually children. I don't see any reason why a toy can't be off limits if others' oreos, candy, soda, happy meals and what not (which I'[m sure is equally as inviting to kids) are as easily off limits. If we don't create boundaries, how will our kids ever learn to respect them (or enforce them or even create them)?
It's fine for you to not wish to let other kids use your family's sand toys; however, it would make things easier for you if you put the toys out of sight when your kids aren't using them. Seems easy enough to do (or even have your kids do before they go off to do something else), and then you could sit and enjoy the paper without interruption.
ETA: Regarding the boundaries issue, the kids we've come across haven't had a problem understanding that while the toys are for everyone, my kids' lunches aren't -- it's just never been an issue. Kids are pretty savvy about that kind of stuff. And I just can't buy into the fact that sharing sand toys as kids will lead to adults who are unable to respect, enforce, or create boundaries, so I can't comment on that part. As I said, whether to share the toys is your call, but it seems like rather than leaving them out and getting irritated, you'd just put them away and make the day go more smoothly.