What are active fin stabilizers mainly designed to reduce while a cruise ship is moving?

Answer: Rolling felt on board

Rolling felt on board ✓ — Right. Active fin stabilizers change their angle in moving water to create heeling moments that oppose roll. Wärtsilä notes that they require forward motion to develop lift, which is why they are best thought of as motion reducers. The everyday analogy is airplane wings in water, not hidden outriggers holding the ship up.

Static dockside safety — Almost, but this overstates the fins. A ship's static dockside capsize margin comes from hull form, loading, GM, and the righting-arm curve. Fins are more like ride-control surfaces: useful for comfort and roll damping while moving, but not a replacement for intact stability.

Displacement and draft — No. Displacement and draft are set by the ship's weight, hull form, loading, and ballast. Stabilizers can add drag and control forces while underway, but they do not decide how deep the hull sits. The ship still obeys Archimedes' principle before the fins do anything.