If it were "yes, love one another", it would require comma after "да" just like in English ("да, любите друг друга").
I believe that in this case "да" is a modal particle and it's used in the meaning "May/let (something happen)". It's a high and a little old-fashioned style.
Similar examples:
да будет свет = let there be light
да здравствует король! (literally "let the king be healthy") = long live the king!

If there were something before this phrase, it could have meant "and" (it's one of the meanings of "да"). For example "Почитайте родителей своих, да любите друг друга" = "Respect your parents and love one another".