Does opponent gain priority when I play a unit in an open state?

No, your opponent does not gain priority when you play a unit in an open state.

According to RiftJudge FAQ #7257, playing units or gear alone does not start a chain, and therefore does not allow opponent reactions or provide a priority window.

Here is the breakdown of how this works:

1. Playing a unit: When you play a unit, it enters the board. Because this action does not start a chain, the game remains in an open state, and priority does not pass to your opponent.
2. "When you play me" abilities: If the unit you played has a "When you play me" triggered ability, that ability does go on the chain. This creates a closed state, which does allow your opponent to react to that specific triggered ability.

In summary, your opponent only receives an opportunity to react if the unit you played has a triggered ability that initiates a chain. If the unit has no such abilities, your opponent cannot react to the act of playing the unit.