Can Brynhildr be reacted to when I play it?

No, you cannot react to Brynhir Thundersong herself being played, but you can react to her "When you play me" triggered ability.

According to RiftJudge FAQ #9147 and FAQ #2757:

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: You play Brynhir. She 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.