John 5:15-18, The man went away and told the Jews that it was Jesus who had made him well. Therefore the Jews started persecuting Jesus, because he was doing such things on the sabbath. But Jesus answered them, “My Father is still working, and I also am working.” For this reason the Jews were seeking all the more to kill him, because he was not only breaking the sabbath, but was also calling God his own Father, thereby making himself equal to God.
Here in this verse after the healing at the pool of Bethesda, the jewish authorities are questioning him and react with violence and seek to execute him for the sin of placing himself in father/son relationship to the father. So here it is clearly perceived as heretical by the Judeans to place yourself in a familial relationship to God.
But as Christ points out in John 10:34, "I say, “You are gods, children of the Most High, all of you;" Jesus's own interpretation of Psalm 82 seems to indicate a precedence for this, but he follows up with "an you say that the one whom the Father has sanctified and sent into the world is blaspheming because I said, ‘I am God’s Son’?"
And in John 1:12, we have the thesis of the Gospel: "But to all who received him, who believed in his name, he gave power to become children of God..."
So it seems that for John, he presents a kind of tension. Believing in Jesus' name (Joshua = only Yahweh saves, not man) seems to be indicate a kind of subordination of mind like a submission to God that enables us to become as God in someway, but through no work or worth of our own.
He states this as a new kind of concept that arrives in Jesus, but then he also says that Jesus is the word made flesh (which, among other things includes the Torah). There are then many theological arguments (like in John 10) about how God is the father and how there is already precedence for this concept and support for it in the Torah. In this way, John indicates that Christ adds nothing new to the Torah on this concept, but is merely correcting an interpretation.
I tend to think that the Johannine jews were a group that had a tradition with many orthodox jewish ties and thought of their relationship to god as parent to child and/or shepherd to sheep. This was in opposition to the majority party of Judeans.
I view this similar to liberal christianity today seeking to expand the net of inclusion to multiple gender identities and sexual orientations while conservative christians tend to reject these ideas as disallowed. Both groups seek back to the ancient documents for support of their takes. Neither group is trying to discard the scriptures, but instead to argue for a better interpretation that the original authors may have thought.
John 5:17 (already quoted above) has this interesting claim that "my father is still working [on the sabbath]." This seems to be a criticism of how the Hebrew Torah says, in Genesis 2:1, "on the seventh day God finished the work that he had done, and he rested". But in the samaritan torah and the greek septuagint, the text says, "God completed in the sixth day the works which he did, and on the seventh day he rested from his works.
Here, the orthodox Hebrew read of the "original language" indicates that "God was still working" (e.g. finished his work on the seventh day and then rested). This seems to be a criticism of the hellenistic (Greek LXX) take on the topic (John 4 has a conversation about samaritan interpretations of where worship should take place with the woman at the well - Mt. Gerezim vs Jerusalem, a major difference in the samaritan vs. Hebrew text).
So to answer your question, it seems like Jesus came to let us all see God as the father, but also to illustrate that this is merely the appropriate interpretation of the Torah (in the original context) and that the majority Jewish opinion had been skewed away from this familial relationship.
So just as with LGBTQ supportive churches and those that ordain women, their arguments are not in spite of the scripture, but because of the scripture. They indicate that this sense of relationship was lost, but was there in the original sense. It really is a doctrinal battle in John. Jesus is the WORD (torah) made into flesh for these kind of doctrinal clarifications. The Johannine community achieved this by saying, "God is on our side," as continues to be done today and through the history of evolving orthodoxy.