Ridiculous! If you let your spouse and children know right form the beginning that you have taken an oath to hold certain things secret and that your are loyal to a certain group...that is completely open and honest about it. This doesn't even only apply to secret societies, take the clearance in government. My father worked at oak ridge national laboratories for may years. He had a top secret clearance, and even now there are some things he still required to be silent about things he did there. Did that affect our relationship? Of course not, most of the things he did had absolutely no bearing on that relationship. Did it mean he was dishonest? Of course not since he was clear that certain aspect of his job were under a certain level of clearance. It is not a lack of honesty to keep silent on subjects that don't concern you. No one knows every detail of another person's life regardless. As a former soldier with a top secret clearance there are some aspects of that job that I was required to keep silent about, and that didn't affect the relationship of me and my fiance or my family. This doesn't even about government jobs either, you see this in business as well. Is a lawyer a incapaible of a honest and open relationship because of confidential information with a client? How about doctors? CEOs of businesses? The world is full of groups where loyalty oaths and secrecy are imperative for the success of that group, does that mean they are inherently wrong for that secrecy? Only people who are paranoid worry excessively about secrets they don't know. This even goes for friendships as well. If a friend tells you something in confidence, should you go and automatically tell your spouse and family what was said? If you do have a open and honest relationship with them you won't tell and they won't ask because they understand that there are different levels of loyalty. Everyone is sworn to secrecy and loyalty to something whether it be spouse, job, friends, whathaveyou, and to suggest that someone can't do an exceptional job because of other loyalties is ridiculous in the extreme. There will always be exceptions, but exceptions are not the rule. It comes down to the person always. If the person is dishonest, they will act dishonest, and if they are honest, the will behave honestly.
"A thing must be understood as certain and true in order to be known without any doubt. But for this reason, that finite knowledge had faults and defects in thy design, therefore hast thou been strangled in thine own doubts" (Paracelsus)