If my opponent controls multiple Shadow characters and I win an intrigue, may I choose a standing character for Kingdom of Shadows' passive effect or must I choose a character that is able to successfully fulfill the effect?

3.6 only applies to triggered effects. So Kingdom of Shadows' passive is not concerned. You can choose any card with a shadow crest, kneeling or standing.

One way to remember this is that 3.6 places restrictions on whether an effect can be initiated or not. A passive effect is going to initiate anyway, so 3.6 doesn't apply.