Royal Caribbean ships do not have topless decks. I believe Carnival is the only one in the cruise line that has this (notice key word "think"). However, from other posts on other sites if she decides to do the thong thing, but leary. Many folks don't want their kids viewing things & apparently fights have broken out on a few ships. (not on Carnival, few on Royal, 2 reports on another cruise line).
But hey, if she wants to go topless! Go for it! Some of the folks that posted above are correct on the beaches & such. Just warn her cuz guys will google at her and anyone with kids might give her dirty looks.