Land, Separation, Clean and Unclean, and Holy Identity
Leviticus uses the same root for God separating Israel from the nations and Israel distinguishing clean from unclean animals. The food laws sit inside a larger theology of a people trained to make holy distinctions.
Where this fits in the story: Leviticus 11's clean/unclean animal distinctions and Leviticus 18's land-vomiting warning are explicitly brought together here.
Where Scripture takes it next: 1 Peter 2:9's holy-nation/peculiar-people language strongly resonates with Israel's separated holy identity, but its most direct scriptural blend is Exodus 19/Isaiah 43 rather than a single exact quotation of Leviticus 20:26.