First, the fourth gospel identifies the beloved disciple as male.
Peter turned and saw that the disciple whom Jesus loved was following them. (This was the one who had leaned back against Jesus at the supper and had said, "Lord, who is going to betray you?) When Peter saw him, he asked, "Lord, what about him?"
Jesus answered, if I want him to remain alive until I return, what is that to you? You must follow me." Becasue of this, the rumor spread among the brothers that this disciple would not die. But Jesus did not say that he would not die; he only said, "If I want him to remain alive until I return, what is that to you?"
This is the disciple who testifies to these things and who wrote them down. We know that his testimony is true. (John 21:20-24; the Greek consistently uses the masculine to refer to the beloved disciple, which is reflected in the translators' consistent choices of masculine pronouns to refer to him.)
Second, the fourth gospel identifies the beloved disciple as someone other than Mary Magdalene when Mary Magdalene speaks with the beloved disciple and is outrun by the beloved disciple and Peter the morning of Jesus' resurrection.
Mary Magdalene went to the tomb and saw that the stone had been removed from the entrance. So she came running to Simon Peter and the other disciple, the one whom Jesus loved, and said, "They have taken the Lord out of the tomb, and we don't know where they have put him."
So Peter and the other disciple started for the tomb. Both were running, but the other disciple outran Peter and reached the tomb first. He bent over and looked in at the strips of linene lying there but did not go in. Then Simon Peter, who was behind him, arrived and went intot he tomb. He saw the strips of linen lying there, as well as the burial cloth that had been around Jesus' head. The cloth was folded up by itself, separate from the linen. Finally the other disciple, who had reached the tomb first, also went inside. He saw and believed. (They still did not understand from Scripture that Jesus had to rise from the dead.)
Then the disciples went back to their homes, but Mary stood outside the tomb crying. (John 20:1-11)
More could be said from early Christian sources outside the Bible, but these should suffice to show that identifying the beloved disciple as Mary Magdalene is poorly researched if not outright dishonest, and that the theory is completely untenable.