What is the word for someone who knows someone else is lying but accepts it
I'm not sure if it would apply where you intend to use it but 'cognitive dissonance' would apply where someone believes two contrary opinions.
For example when a person knows their spouse is cheating on them but also refuses to believe their spouse is cheating that person is experiencing cognitive dissonance.
Such a person is compliant or complaisant
Willing to please others or to accept what they do or say without protest