No less than seven "Jesus fulfilled a biblical prophecy" claims are made tied to T'hillim / Psalm 69. This is the second of those seven claims.
Yet, the psalm states that the subject is a sinner. "O G-d, You know my folly, and my acts of guilt are not concealed from You." T'hillim / Psalm 69:6.
If Jesus is "without sin" this psalm is not about him and all seven of the claims fall apart before they begin.
This psalm is a poem written by King David about himself. It is autobiographical. T'hillim / Psalm 69:1 begins "For the conductor, on שׁוֹשַׁנִּים / shoshannim, of David." (שׁוֹשַׁנִּים / shoshannim are roses and this is a poetic way of speaking of the Jewish people who were David's roses).
The claim is tied to T'hillim / Psalm 69:9 (8 in Christian versions which either do not print the first line quoted in the previous paragraph, or do not number it). "I was stranger to my brothers, and alien to the sons of my mother."
The list maker claims that Luke 8:20 - 21 "fulfills" this sentence (which is not a prophecy). Yet Luke 8 says no such thing. "And he was told, “Your mother and your brothers are standing outside, desiring to see you.” But he answered them, “My mother and my brothers are those who hear the word of G-d and do it.”
Jesus is not saying these people are strangers to him -- he is saying that he considers his followers to be his family. The interesting (unspoken) claim here is that Jesus' own family do NOT believe in him.
A Christian should really ask himself WHY his own mother and brothers would not be counted among his followers. . . it should make them question Jesus' claims. . .
That aside, Luke 8 in no way even infers that his mother and brothers were unknown to him -- strangers.
Read the psalm. Don't just let the list maker take a partial sentence out of context.
The psalm makes it clear that David is talking about how he is surrounded by enemies even though he has done nothing wrong.
Ask yourself: did Jesus' mother or his brothers hate him? "Those who hate me for nothing are more numerous than the hairs of my head; mighty are those who would cut me off, who are my enemies because of lies; what I did not steal, I will then return." T'hillim / Psalm 69:5.
What lies did Jesus' mother and brothers believe about him -- what did they think he stole or lied about?
Does that passage "fit" Jesus? Note that it isn't speaking of some strangers (e.g. the Pharisees who supposedly wanted him dead) -- but of family and close friends. Even though the Christian bible says that one person turned on Jesus (Judas) it never states that lots of people who knew him hated him, even his own family. . .
But that is a true statement about King David.
The passage does fit King David, the author. As a child David was set apart from his brothers because he was thought to be the product of his mother's adultery. The introductory verse (a psalm of David) points to this being autobiographical. The Malbim (R' Meïr Leibush ben Yehiel Michel Wisser, 19th century) interprets the psalm about King David and about the Jewish nation in exile -- it fits both.
The timing of this psalm is when King David was running, in fear of his life, from his own son אַבְשָלוֹם / Absalom. Absalom (David's third son) crowned himself king and revolted against his father -- forcing David to flee from Jerusalem. David had sons by several wives. One son, Amnon, raped his sister Tamar. Absalom (as mentioned) turned against his father, David, trying to wrest the kingdom from him. Absalom was killed in battle.
One can certainly see how David would say he was a stranger to his brothers -- both his actual brothers and his own children. (Remember, psalms are poetry so it isn't necessary for David to name everyone involved -- he is making a point). David has spent most of his life being alienated from his own family -- hence the line: "I was stranger to my brothers, and alien to the sons of my mother." T'hillim / Psalm 69:9 (8 in Christian versions).
Our sages also say that Israel's brothers -- Esau and Ishmael (the Christians and the Muslims) have been strangers to us -- often killing us and rejecting us. Thus the psalm is applicable, in a more midrashic (allegorical) way to the Jewish people.
But it does not "fit" Jesus who was never a stranger to his mother or brothers. They never turned on him (as Judas supposedly did) -- indeed his mother is supposedly one who goes to his tomb after he is dead. . .
Rabbi Yaacov Haber discusses the historical background, context, plain meaning (p'shat) of the psalm at the Yeshiva University online site. Link. Study the psalm as a whole -- learn a little of David's personal history (found in the T'nach) -- and realize that the missionary ploy of taking a partial sentence out of context to make something seem to fit Jesus does not work when one actually looks at the context of that sentence.