I know that both Royal and Carnival will check the National Sex Offender Registry. Disney, Princess, and Norwegian do not have any restrictions at this time. And most River cruises and cruise lines outside the US don't do checks, but in those cases you have to get into the country to be able to sail anyway. And as a Sex Offender I have to let the government know 21 days before travelling out of the country and they send a letter to any country I am visiting letting them know I am coming, when and I believe how as well.
As far as the cruise lines are concerned though, if they are OK with letting me onboard that is their business for the cruise. They don't let the foreign country know, that is left up to the government. So, whether another country will let me in or not is their business, not the cruise ships.
I'm not really asking for legal advice here, I am just trying to gauge what other people may have observed as far as people in my position. I can go ask 5 lawyers today and get 5 different answers, what it will come down to is the person who actually intervenes at the boarder. And if people have seen that they are more laxed or more strict, I'd like that info. I know that no matter what someone says here, it isn't going to be a hard and fast rule. I have seen people get Visa's to a country and then get turned away when they arrived by plane. I just haven't heard much about cruise ships and would like to get an idea of where I stand before I book the cruise.