Omar6741 said
Is there any plausibility to the traditional view that the “brothers” of Jesus mentioned in the New Testament were actually his cousins?

  

Of course there is “plausibility”–based on the success of the highly influential essay by Jerome, the Perpetual Virginity of Mary which you can read here:

** you do not have permission to see this link **

It became the consensus position of the Roman Catholic Church, and remained so for a very long time. But Dr. John P. Meier (who died last week, a scholar and Roman Catholic priest in good standing, ** you do not have permission to see this link **) argued persuasively that “it is difficult to maintain that the brothers are thought of only as step-brothers or cousins of Jesus…” Here is an extended quotation of some Meier’s truly world class redaction criticism:

“Matthew often points forward and backward in his text to foreshadow and recapitulate. Such is the case here. The author who tells us in 1:25a that Joseph did not have relations with Mary until she bore a son is the same author who tells us in 13:55 that Jesus’ mother is called Mary and his brothers James, Joseph, Simon, and Jude. Putting aside for the moment the special question of the meaning(s) of “brother” in NT Greek, we must admit that, at first glance, the combination of the “until” statement in Matt 1:25a with the naming of Jesus’ mother and brothers all in the same verse (13:55) creates the natural impression that Matthew understood 1:25a to mean that Joseph and Mary did have children after the birth of Jesus.

This initial impression of the redactional intention of Matthew is strengthened when we examine the way Matt 13:55 recasts Mark’s version of the question hurled at Jesus by the unbelieving townspeople of Nazareth. In Mark 6:3, the citizens of Nazareth ask: “Is this not the woodworker, the son of Mary and brother of James and Joses and Jude and Simon? And are not his sisters here with us?” Notice the structure of Mark’s questions: there is no mention of Jesus’ father; the designation “woodworker” (applied to Jesus), the name of the mother, and the name of the four brothers are all placed in one question; and the (unnamed) sisters are referred to in a separate question. In Matthew, things are sorted out differently. First, perhaps in deference to Jesus’ dignity, Matthew shifts the slur about being a mere woodworker to Jesus’ father. But since Matthew has made clear in the Infancy Narrative that Joseph is merely Jesus’ putative father, the reference to the (unnamed) father is cordoned off in a separate question: “Is this not the son of the woodworker?” (13:55). Then, beginning a separate question, Matthew puts together and names—apart from the putative father—the mother and brothers of Jesus: “Is not his mother called Mary and his brothers James and Joseph and Simon and Jude?” The one mother and the four brothers, treated separately from Jesus’ merely legal father, are all the subject of the one verb, “is called.” Then, as in Mark, the unnamed sisters are mentioned by the androcentric audience as an afterthought: “And are not all his sisters with us?” Thus, simply on the level of Matthew’s redaction, it is difficult to maintain that the brothers are thought of only as step-brothers or cousins of Jesus…”

“The brothers and sisters of Jesus in ecumenical perspective”
By: Meier, John P. Source: The Catholic Biblical Quarterly, 54 no 1 Jan 1992

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There is a big difference between plausible and probable. As I recall, the Greek word for “brothers” is used in the LXX to refer to cousins sometimes; however, in the context of a close, critical reading of Mark and Matthew, Jesus’ “brothers” were probably not his cousins.