Why modern navies still train and equip boarding parties

Do navies still carry equipment for boarding actions, and when was the last contested boarding?

Yes. The historical reference for contested boarding is World War II, while later boardings of merchant vessels continue for maritime-security purposes.

Navies still carry the capacity to board other vessels because merchant shipping remains part of their work at sea. Piracy and terrorism are two reasons given for retaining that capability. A contested boarding in World War II supplies the historical reference, while many subsequent boardings are acknowledged. No particular wartime action is named.