Having less pressure against unorthodox or novel positions is a good thing. But I think it makes sense to have minimal social pressure to give some account of apparent discrepancies between actions and beliefs-- since it suggests (though doesn't necessitate) contradictory beliefs somewhere.
This seems to act as an incentive for both resolving the conflict, and for obscuring its presence or nature. I feel that the latter effect can be more damaging, so it might be safer to avoid this pressure. For example, drawing of attention to the presence of an apparent conflict (if it's plausible that it has been missed) that isn't accompanied by (implied) disapproval.
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.