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Can you use Ivory Kingdoms Unicorn's reaction ability if one of your characters has lost the duel against Kakita Yuri? I.e. can you still resolve the part of the effect that lets you immediately declaring the next conflict but the conflict having to have the original type of political rather than military? (assuming that you have a political conflict remaining to declare that is)

You cannot trigger Ivory Kingdoms Unicorn’s ability if you have lost Kakita Yuri’s duel this phase. Because the rhino’s ability states “that conflict is [MIL] instead of its normal type,” you are declaring a military conflict which Yuri’s duel’s effect prevents you from doing.

[Tyler Parrott, Apr 23 2019]