The cruise ships have all the passengers passport information already and can provide this info to the port of call well ahead of time.
There may be one or two passengers that customs would be interested in talking to but that would be it.
I have been on many cruises to many countries and have seldom produced my passport to go ashore, and when you did produce it, it was just a passing glance from a customs official.
Some places require a visa to enter but these are done well ahead of time and the cruise line has the paperwork.
The requirement for a PCR test will be over shortly, with the opening of the land border to the US not requiring any prior test, the Canadian government is being pressured to drop this requirement.