Jesus is clearly indicating that real authority to represent the Supreme Being comes from God. This authority comes through a relationship of loving service to God - as clarified by Jesus here:
"I know that you do not have the love of God in your hearts."
This authority comes from pleasing the Supreme Being. Making an "effort to obtain the judgement (or opinion) that comes from the only God" means to please God. Jesus illustrated that God was the source of his own authority, and pleasing God was his central objective:
"By myself I can do nothing; I judge only as I hear, and my judgment is just, for I seek not to please myself but Him who sent me." (John 5:30)
Jesus indicates that he can see these temple officials are not thus empowered, and are not seeking to please God. They obtained their authority by pleasing others within the temple hierarchy.
How ironic it is that the very people who say they represent Jesus today have assumed the same process that Jesus condemned here in this statement. Those popes, cardinals, bishops, priests, ministers and reverends who have been politically appointed to their positions in a particular church or sect have gained their positions by pleasing those in the church hierarchy (each other, in other words). Then they collect salaries from tithings, turning what is supposed to be service to God into a business arrangement.
This has nothing to do with loving God and teaching love for God on behalf of the Supreme Being and in the Name of the Supreme Being, as Jesus did, and all the prophets did.
Furthermore, the word "believe" here is not an appropriate translation. The word πιστεύω (pisteuō) means to "have confidence in" or be "entrusted." It means to trust. Jesus is speaking of trusting in the Supreme Being: Giving one's life to the Supreme Being and taking shelter in Him. This is what Jesus had done - and the reason Jesus could represent the Supreme Being.
This also ties in with, "I have come in my Father's Name." To come in someone's name means to represent that person: But it also highlights the potency or power of that person's name.