It doesn't look as if Lola is coming back, so I guess we can talk about theory.
If you mean by identity, that women need to be with men who identify as men in order to feel feminine, this is not true. Hetero women want to be with men because this is the way they are wired in just the same way that hetero men do not get turned on by other men. If GGs are not hetero, they are lesbian (or bi) and they have no issues being with women.
Women don't want others to know their husbands are CDers for the same reasons that CDers are in closets. It's because of the bias that exists in our society, and the fear they, their husbands, and their children will be ostracized by those in their immediate circles.
First, this is not a tirade, it is real emotions of surprise and fear that emanates from a woman who is in shock that her husband is not who he had presented himself to be. Second, you mention a CDer minimizing things to his wife and this is not OK in a committed relationship. A partner feels lied to when this happens, and she feels betrayed with the knowledge that her husband kept an important part of who he is from her. She feels as if she has been living with a stranger and she wonders what else he is not telling her. And if the husband cannot tell his wife where "things will wind up", how can she live without worry, wondering if this will lead to wanting to live full time after retirement, given both truths, that she is not wired to be attracted to women and there is a degree of bias in our society towards men who live as women.
I'm not saying that no woman can stay the course at all. I'm saying there is a long journey ahead for any wife who did not know about this from the onset, that is fraught with conflicting emotion and redefinition of what is gender and sexual orientation. A GG not only needs to redefine her husband and their relationship, she needs to redefine herself.