Manipulative Games People Play
Duplicity is contradictory doubleness of thought, speech, or action. See Merriam Webster definition
When a church (cult) expects you to be "honest in your dealings with your fellow man" in order to acquire special access to religious rights and acceptance, while that same church routinely lies, misrepresents, or omits significant information in its representations, duplicity is manifested by the organization, and by the leaders of the organization, individually, for failing to call it out, or failing to support a legitimate criticism or critic on these grounds.
Dishonesty is dishonesty in all its forms.
See LDS Personal Faith Crisis Report: A typical statement by a 35 year old male who comments on the credibility of the LDS Church in view of its requirements of honesty from its members.
Individuals may be duplicitous when they represent that they want to have an honest and friendly relationship with you, while expecting you to overlook that they routinely undermine you or stab you in the back or avoid legitimate discussions about having done so in the past.
See: Sample Dialogue from Grey Ribbon Management Techniques.
Also see Social Engineering