Yes cruise ships do pollute the oceans they travel on because they will dump the human waste out into the ocean once they leave the dock.
When the cruise ship gets out into the ocean and has waste such as poop and urine and shower water etc the cruise ship dumps that waste out into the ocean which then pollutes the ocean waters.
Around 210,000 gallons of human waste and sewage is dumped into the ocean from a cruise ship.
Cruise ships which pollute the oceans waters ply the waters off our coasts, producing and then dumping large amounts of sewage and other wastes into our oceans, polluting our beaches, contaminating our coral reefs, and destroying our valuable marine ecology.
Going on a cruise ship is a nice vacation but if you're against harming the environment then a cruise on a cruise ship may not be for you.