From a Protestant perspective, Christian Authority is not as important as Scripture, which is, in fact the only true authority for the Christian.
The westminster Confession of Faith, one of the major documents to come out of the Reformation, states this:
IV. The authority of the Holy Scripture, for which it ought to be believed and obeyed, dependeth not upon the testimony of any man, or Church; but wholly upon God (who is truth itself) the author thereof: and therefore it is to be received because it is the Word of God. (Chapter 1, section 4.).
This does not totally negate all human authority or authority in the church, however. This includes both ecclesiastical and secular authority.
Regarding church authority, in the Biblical book of Hebrews, Christians are told to: "Obey your leaders and submit to them, for they are keeping watch over your souls, as those who will have to give an account. Let them do this with joy and not with groaning, for that would be of no advantage to you."
As to secular authority, in the book of Romans, Christians are told:
"Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God."
So, the idea, for Protestant Christians, is that they should obey the leaders placed over them, both secular and ecclesiastical, unless those leaders are commanding something contrary to Scripture.
Here's an example: When the Apostle Peter was told by the governing authorities that he could no longer preach the Gospel, this was the response: But Peter and the apostles answered, “We must obey God rather than men." (Acts 5:29).