Can you react to a second unit being played to a battlefield?

Ruling: No, playing a unit does not grant priority, so you cannot react to a unit being played to a battlefield.

Nuances:

• If your opponent scores a hold point and moves a new unit to the same battlefield while maintaining control the entire time, you cannot react
• If your opponent loses control of the battlefield and then moves back in, it triggers a showdown (even though it can't result in a conquer), which does allow for reactions since control is potentially changing
• You cannot conquer a battlefield you scored that turn, regardless of what happens between those states