This feast came new to Lutheranism in Lutheran Book of Worship as "St. James, Martyr" but was rejected by Lutheran Worship. I think LBW got it from the American revision of the Book of Common Prayer. The feast is again left out of the ELCA's newest hymnal, Evangelical Lutheran Worship. If it has any history in modern German Lutheran hymnals, I am unaware of it but would happy to be corrected.
Lutheranism is, of course, part of the Western Church - indeed, in accordance with our own self-understanding, we should really say that Lutheranism is the continuance of the Western Church cleaned up from certain errors (the three P's: Purgatory, Prayer to saints, and the Pope's lavish claims), by the grace of God. In the West, the James who is denominated as "the brother of the Lord" has usually been considered as identical to "James the son of Alpheus." Read all about it. Consequently, in the West, "James, the brother of the Lord" is celebrated on May 1, the Feast of St. Philip and St. James (the Less, the Just, son of Alpheus). In the West, there is no feast of any St. James on October 23.
In the Eastern Church, however, the judgment has been different. They identify "James, the brother of the Lord" as someone other than one of the apostles. Namely, as one of four children of Joseph of Nazareth from his first marriage. The evidence for this comes from the Protoevangelium of James. Read all about it. His day in the East is, indeed, October 23.
Including this feast day in a Lutheran calendar is, therefore, a bit polemical. It makes a definite statement about which James is which, and it is a statement contrary to the West's tradition.
Secondly, to modern American ears the name of the feast is a bit polemical in another way. When the East calls James "the brother of the Lord" they mean one thing and modern Protestants, like the Anglo-American Common Prayer mean quite another.
[Here in passing we might note another title in LSB that was not adopted in DDSB: St. Mary, "Mother of our Lord." This was, in my opinion, a most unfortunate choice. In the Ecumenical Creeds and our Lutheran Confessions, and in all the old Lutheran calendars, she is "Mary the Bearer of God (Θεοτόκος, Gottesgebaererin)" or "the Virgin Mary" or "the Blessed Virgin Mary." To those with any church history, the title "Mother of Our Lord" is fraught with meaning as it was the title that Nestorius insisted upon using, and no other. If using the Confessions' title of "Bearer of God" was thought to be too difficult or confusing for today's laity, then why not just "The Virgin Mary" as she is called in the Creed? Or just "St. Mary"?]
Well. Isn't it all adiaphora? Who cares whether one thinks that the West or East is right about which James is which? Indeed, they might both be wrong and we could add a couple other James' Days to the calendar. But it's precisely the fact that this is a judgment call that made me most hesitant to add the feast. When in doubt: dance with who brung ya. We're a Western Church. Likewise with titles given to Mary - let's stick with our own tradition. Same thing when it comes to Mary and "the brothers of the Lord." If you really think the meaning of that term is adiaphora, then why would you go out of your way to proclaim an opinion contrary to the whole history of the Church? It it doesn't matter then honor your fathers in the faith by accepting their opinion.
So I suppose this is a matter of general outlook. And my outlook is this: let's not reinvent the wheel and let's be content with what our own fathers have handed us.