Suppose you're a school principal looking to hire a new Judaic studies teacher. There's a certain fellow, X, you'd like to hire, who you think is well qualified and well suited for the job - in fact, you consider him the best person available. However, X subscribes to beliefs p and q, and the majority of the school board - the people who hired you - mistakenly believe p and q to be heretical. They therefore would feel that X was unsuitable for the job. (We will leave aside whether they actually consider him to be a heretic.) Should you hire X, because your mandate is (let's assume) to ensure your students get as good an education as possible, and your job is to pursue that goal to the best of your ability, or should you hire someone else, because your employer won't like the particular decision to hire X?
(Assume that (a) you cannot disabuse the board of their incorrect opinion regarding p and q; and (b) if you get fired, you're confident of landing on your feet without trauma to yourself or your family.)