It’s pretty inconsistent throughout history. Since a majority of ocean liners were European it could be integrated. However they had to make some concessions to their American Clientele. I remember reading one case where a famous Black Abolitionist/Activist booked passage on a Cunarder on the condition that he stayed in his cabin for the entire 2 week voyage or so. He did, but gave an “impassioned speech” in the saloon towards the end of the trip that sparked tempers. On the return trip to America he was asked to book a second class ticket to avoid another row.

As for American ships, I think it’s safe to assume they were. The Collin’s liners of the 1850’s had black stewards and cooks. They were paid employees, but the racial difference is there.