All foreign tourists are allowed to enter Russia provided they have the proper documents.
According to the Russian law regarding the non-visa cruise passengers the proper documents are:
1) A valid passport, 2) A photo copy of your passport 3) A proof of your participation in a tour program arranged by a licensed and authorized operator. First two you shall provide yourself, and the third one shall be provided by us. It is an authorized tour ticket, which we will send you by email. Sometimes our clients say that ships try to control disembarkation process stating that all those passengers having made their own independent arrangements must wait until the ship's own excursion passengers have exited first. The ship has no right to hold its passengers aboard against their will. In fact there is no difference for Russian Сustoms between passengers booked with ship sponsored excursion and passengers booked with a private one. That means you can disembark at the time specified in your tour ticket.