What makes the naturalistic, secular humanistic, and atheistic existentialistic worldviews differ from the Christian worldview in regard to family?
In a sense, part of the difficultly with the question is that it assumes the existences of a uniform Christian worldview concerning family. This assumption is false. For example, many Christian churches in Africa accept polygamy and approve the criminalization of homosexuality whereas many Christian churches in the OECD perform gay marriages and do not accept polygamy. Some Christian groups even in the US force very young girls into polygamous marriages.
Many non-religious groups would argue that people's personal and family activities, so long as they are non-coercive and do not involve child abuse, are really a matter of individual conscience. There is no single model of family advocated by the diverse groups you list, but rather the notion of freedom of individual choice, including the freedom to have permanent monogamous relationships.