As for Castaway, the beaches are very clear of debris. And the sand is raked and fairly well packed. Very pleasant beach break.
I actually expect it to occur in Cancun, Cozumel, Costa Maya (well, they are all close - and basically one big bay). I cannot remember a visit there when I haven’t seen some.
And unless Disney owns a property, I would not have the same expectations.
If it is a turn-off, I would look at an Eastern Caribbean itinerary. It doesn’t seem to have the same problem (this is my perception, not a scientific record; take it with a grain of salt).