I think that if there are positions that you can't argue... then the responsibility is probably to resign. If one's own conscience is opposed to the requirements and responsibilities of the job, then it's time to leave the job.
“When you want a thing done, 'Don't do it yourself' is a good motto for Scoutmasters.”
“Unless you're willing to have a go, fail miserably, and have another go, success won't happen.”