Can Brynhir Thundersong be reacted to?

The short answer is: You cannot react to Brynhir Thundersong herself being played, but you can react to her "When you play me" triggered ability.

According to the official FAQ (ID 2757) and the game's chain rules:

1. Brynhir herself: When you play Brynhir, she resolves immediately to the battlefield. Because units resolve as soon as they are finalized to the chain, there is no window to play a reaction to the unit entering play.
2. Her "When you play me" effect: Once she is on the battlefield, her triggered ability goes on the chain. This is a separate event that you can respond to with reactions.

Sequence of Events

• Step 1: Brynhir is played and resolves immediately to the battlefield.
• Step 2: Her "When you play me" trigger is placed on the chain.
• Step 3: Players have an opportunity to play reactions in response to this trigger while it is on the chain.
• Step 4: Once the trigger resolves, its effect (preventing opponents from playing cards for the remainder of the turn) takes hold. After this point, opponents can no longer play cards.

Important Nuance: As noted in FAQ 8446, you cannot use a card like Not So Fast to counter this ability because it is a global effect that does not target a specific unit or gear. However, you can use other reactions (such as activating a hidden ability) while her trigger is still on the chain. Once the trigger resolves, the restriction is absolute for the rest of the turn.