Are air tags allowed on a cruise ship?

They are, but you will have your luggage with you, except for the brief period when you check in and wait for the bags to be delivered to your room......unless you are worried that the bags might still be on the dock when the ship starts moving.

As Bob Timmons says, there should not be any restrictions. They will be fine for travel to and from your cruise. However I think you might find AirTag performance is patchy and intermittent while on board because the ship’s steel structure might block signals.