Q: How does Ret. US Supreme Court Justice Breyer propose to "...decide cases in a way that will prevent social discord stemming from religion"?
Law Professor Daniel Gordon  describes the approach by the term Consequential Thinking and compares three justices and their approach to interpretation of the Constitution by focusing on Justice Breyer.
Breyer warns that the relation between government and religion is one of separation, not social conflict, creating mutual hostility and suspicion. To assure that the Establishment Clause maintains the delicate balance between neutrality toward religion, not hostility toward religion, Establishment Clause cases remain exercises in legal judgment based not only on the social conflict avoidance purpose of the Establishment and Free Exercise Clauses, but also on consequences measured in light of that social conflict avoidance purpose.
Other than McCreary County (mentioned due to Breyer's deciding vote), the cases represent compromises between government actors and the religious beliefs of individuals and religious organizations. In effect, the compromises allow governance while also allowing individuals and organizations to continue participating in society without greatly sacrificing their religious beliefs.
From Law Professor Frank S. Ravitch, specific to Van Orden and McCreary County,
In both Van Orden and McCreary County, eight justices split 4-4. Justice Stephen G. Breyer provided the deciding vote to uphold display of the monument in the Texas case and invalidate the displays in the Kentucky case.
Several themes emerge in Breyer’s concurring opinion in Van Orden.
First, he viewed this case as a “borderline” one in which no legal test could be appropriately applied.
Second, Breyer, like the plurality, found that the purpose of the establishment clause is to maintain some level of separation between church and state while avoiding hostility to religion—although it seems clear that Breyer weighed these factors differently than the other four.
Third, Breyer asserted that avoiding religious divisiveness is a major goal of the establishment clause. Therefore, the type of religious purpose on view in McCreary County was unconstitutional, but so would be attempts by the government to remove all religious symbolism from the “public sphere.”
Fourth, Breyer argued that long-standing religious displays do not generally raise the same concerns as new attempts to display religious objects, because the long-standing displays are less likely to be divisive, assuming their context and purpose adequately secularize them. This point seems to be an attempt to protect against establishment clause challenges to most long-standing displays that include religious themes.
1 Examining Justice Breyer's Constitutional Consequential Thinking: Can Justice Scalia Be Wrong and Justice Kennedy Be Right?