Its very easy for the rich and famous to vacation with "regular folk" Most rich and famous have a "public look" or trademark ie a female celeb may always wear her hair in a certain style and always wear makeup in a certain way. Then in her regular day to day life with family , out of the public eye, she wears her hair in a different way. People may still recognise her but because she doesn't look the way they associate with her, she blends in and people don't realise she who she is. Or they may a different style of clothes or not have an army of security personnel around them.
On a cruise ship for example, there will always be a suites, which may have private dining areas. They may also have all sorts of private services, eg a private bar, or a shopping service or private tours and excursions in various ports. They will probably have a special check in area and luggage service as well.
Its the same on flights, rich and famous celebs fly on regular commercial flights but us regular folk never see them. They will have a separate check in area, they may have a special boarding area, they may board last and get off first, they may go directly out of the airport without collecting their luggage, which will be delivered separately to their hotel. For international travel, the passport check person may even get on the plane and check passports before the rich and famous person even leaves the plane.