In all dispensations, the “Chosen People” have had to face a time when the promises of their fathers were extended beyond those familial ties and given to others that previously had been denied a place at the table of the chosen patriarch. That necessitated moving past the former paradigm of restricted family access to a new paradigm that focused on a broader family. Doing so in the early Church caused great disputations (from the “House of Israel” to include uncircumcised Gentiles in the "Body of Christ"). This tension was evident even earlier in Jesus’ ministry, when He told the Jews that God could raise up children unto Abraham from the rocks - that it wasn’t their literal lineage that would save them.
Ultimately, the most unifying familial designation available to us is summed up in a simple Primary song: “I am a child of God.”
Just to chew on: If we were to begin a modern focus on the “House of Abraham” (instead of the House of Israel), the familial tension that currently exists between Mormonism and Islam would disappear doctrinally. If we were to begin a modern focus on simply the “House of the Living God,” the familial tension that currently exists between Mormonism and Hinduism or Buddhism or any other -ism would disappear doctrinally.
(I absolutely love the doctrine of familial adoption. I really do. I think it is incredibly powerful and uplifting. I also will not advocate for a change in the way we express that adoption. I am totally serious when I say that there might be an actual power that has been given by God to the House of Israel; there might be an actual power in the recorded birthright descent that is important to the gathering of a people who are adopted into that lineage. There might be a valid reason to keep the current focus on the House of Israel. If the prophets never change our focus in this regard, I will not complain or be disappointed. I will accept it completely. I simply am open to a different adoptive phraseology if it ever comes time to “adopt” it.)