Not even close. James, son of Alpahaeus is Matthew the Apostle. Those that associate him as James the Just are mostly the Catholics and follow the opinion of Jerome and Hippolytus simply because they both were stoned to death. If that is the litmus test, then Stephen fits that description as well. The Jews stoned people.
There goes your "universal acceptance" that there was a James who was the Lord Jesus Christ's biological brother from Jesus' birthmother Mary.
Not quite. Outside of the Catholics and Eastern Orthodox, the Protestant church accepts James as the brother of Jesus, as was Jude, Joses, and Simon. The most significant source is Paul in his letter to the churches in Galatia and Corinth. Next is Luke in the Acts of the Apostles. His list of blood-related brothers comes from Matthew and Mark where they list his mother, brothers, and mention sisters. This is not a cousin nor generic 'bretheren' but physical relations. Whether they were kin from a never mentioned previous marriage of Joseph is also, NEVER mentioned. The simple fact that his blood family is listed should end all controversy, but the Catholic church insists on worshipping Mary.
This is the Mary known from antiquity as Aeiparthenos (Greek: ἀειπαρθὲ) or Semper Virgine, in both languages, literally 'Ever-virgin'.
Once again, following man's tradition vice the Word of God. NOTHING in scripture says Mary was a perpetual virgin. Isaiah prophesied that "A virgin shall conceive..." which is what happened. But here is the biological truth, virgins can conceive on their first try! But they don't remain virgins.
Welcome to the party!