Moral flexibility is just what it sounds like. It describes people who are "flexible" with their moral values. It is basically a nice way of describing someone with no moral ethics. The whole idea of moral value is a foundation for your belief system. It is not only a religious idea. If someone screws you over and that makes it okay to screw them over. That is a belief system. Someone with moral flexibility would waiver on that, depending on the situation, who's involved, what the insult was, etc, etc.
I do not defend moral flexibility. I don't believe in it. It basically is a belief that everything is relative and that people can be left to do what they "feel" is right. It also enables people to institue morals when convenient. Always tell the truth, unless it's going to hurt you, then it's okay to lie. The point of that statement is really, it's okay to lie, and it's up to each person to decide when the right time to lie is.