Can you react to a unit being played into a battlefield with a reaction spell, and if so, would removing the controlling unit with Gust prevent the new unit from being played there?

Ruling: You cannot react to units being played. Permanents do not give priority windows to respond to.

Nuances:

• Units with triggered effects (like Draw 1 or Deal damage) do create a reaction window when their trigger goes on the chain, but the unit is already played at that point
• There is no way to block a unit from being played into a battlefield; you can only remove it afterwards
• Even if you could react to a trigger and remove the controlling unit, the new unit would already be at the battlefield