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I think it's fairly heavily implied several that Mat actually did want to sleep with Tylin, he's just afraid that Beslan will try to murder him if he does. He stops protesting the relationship once Beslan tells him it's ok, although he continues to hate the fact that he's only viewed as a plaything instead of a person.

None of that makes the actual rape that already happened any more acceptable, but it does somewhat explain Mat's changing attitude towards Tylin.

Back on the topic of Nynaeve, she wasn't actually the one who made light of the situation with Mat and Tylin. That was Elayne who is a terrible excuse for a human being.