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I have a White Knight in play, AI casts Gelid Shackles on it. Next turn it casts a second shackles on it. On my next turn I equip the knight with Swiftfoot Boots. I think I understand that the shackles stay, since they were cast before the knight got hexproof. However, the AI is activating them to make the knight Defender and that is the part I wonder if it should be happening.

The activated ability of Gelid Shackles isn't targeted, therefore it's unaffected by hexproof which prevents the targeting. So its working as it should.