Accepting such a job would then involve a compromise of fellowship principles. Other cases may be unclear, such as some teaching or coaching positions. In such cases a person should examine each situation on its own merits or demerits. What are the requirements of the job. We cannot necessarily assume that the requirements of the position are the same as they would be for a similar position in our churches.
Ambiguous situations are sometimes a matter of judgment.
Two Christians in very similar circumstances may come to different conclusions. As stated earlier, in such situations we should be cautious about judging the decisions made by others. Doubtful cases are not a wise place to exercise church discipline. He's not interested in changing his beliefs. You are right when you say that we cannot pick and choose what to believe in the Bible.