Do not give dogs what is holy;
and do not throw your pearls before swine,
lest they trample them underfoot
and turn to attack you.
Dogs and swine are unclean animals; Romans and pagans are uncircumcized, inherently unclean human beings. This saying does not seem at all to stem from a sense of universal brotherhood.
It could be read with a different perspective, of course. Readers of Lord Dunsany will remember that the Witch who lives at the edge of the world keeps a herd of pigs; and employs poets to keep them fed. What do the poets feed them? -- Pearls, of course. Do the pigs like their pearls? -- Someone asks. "Not particularly." So this could be an example of treating people as they would like.
Is that Jesus' meaning here? It seems unlikely; to this extent he talks like a typical Israelite of his day; and outreach to the goyim does not seem to become a priority of his movement until after his death.
His constituency is the oppressed poor of Israel; and their oppressors are Romans and their local clients. When he is eventually executed, it is done by the Roman authorities on the recommendation of the High Priest and his party, people who support and benefit from Roman rule, at the expense of the peasantry who make up the vast majority of his nation.
Although Jesus is portrayed elsewhere in the gospels as enjoying friendly relations with sympathetic foreigners, that may not be at all what he expected at the beginning of his career.