How should Hosea 8:4 be reconciled with passages stating that all authorities are appointed by God?

Even rulers appointed by God make serious errors which sometimes need to be opposed. A good example is that of Jeroboam I, who was chosen to rebel against King Solomon. According to 1 Kings 11:

27 This is how he came to rebel...29 Jeroboam left Jerusalem, and the prophet Ahijah the Shilonite met him on the road... 30 Ahijah took off his new cloak, tore it into twelve pieces, 31 and said to Jeroboam: “Take ten pieces for yourself. Thus says the Lord, the God of Israel: I am about to tear the kingdom out of Solomon’s hand and will give you ten of the tribes.

This shows that even though Solomon was given God's authority as king, God also authorized Jeroboam to rebel against Solomon. Later, after Jeroboam became king of (northern) Israel, prophets spoke out against him and the temple he established at Bethel. Later, the prophets Elijah and Elisha conspired to overthrow the dynasty of Ahab and install Jehu as king. This too shows that God may inspire rebellion against royal authority.

But did the standard change in the NT age? The context in Romans 13 is a situation shortly after Jews, including Jewish Christians, had been expelled during the reign of Emperor Claudius (49-50 c.e.). This is mentioned in Acts 18:2 where Paul meets with Aquila and Pricsilla "who had recently come from Italy with because Claudius had ordered all the Jews to leave Rome." Paul urged Christians not to resist Roman rule, specifically that they should pay taxes (vs. 7). But we must ask: would he go so far as to instruct them to offer sacrifices to Roman gods, as the state would later require? One hopes not. Would he tell Catholics in England to renounce the pope as required during the Cromwell regime, or tell Protestants in France to accept papal authority? For that matter, would he expect Jewish Christians to renounce Christ if ordered to do so by the authority of the high priest? Clearly there are times when the demand of conscience trumps that of external authorities.

Conclusion: The statement “there is no authority except that which God has established” is not meant to suggest that all orders given by secular authorities must be obeyed. Paul urged Christians to pay their taxes and generally act in accordance with Roman law. But when push came to shove - a few decades after Paul's writing - Christians would rightly put their consciences first and resist Roman authorities who required them to offer incense to the gods of the State.

Consider Moses and Pharaoh. Though by no means perfectly following God's will, Moses lead the people of Israel by following God's call to lead Israel. On the other hand, Pharaoh wouldn't even acknowledge Yahweh (Exodus 5:2) much less willingly do what God wanted. Both carried out God's will but in vastly different ways.

When you look at the context of Hosea 8:4, Israel (the northern kingdom) had not followed God and thus did not seek God's will in appointing their leaders. They worshiped idols. Thus, they accomplished God's will in many ways more like Pharaoh rather than Moses.

Put the trumpet to your mouth! Like an eagle the enemy comes against the house of Yahweh Because they have trespassed against My covenant And transgressed against My law. They cry out to Me, “My God, we of Israel know You!” Israel has rejected the good; The enemy will pursue him. They have set up kings, but not by Me; They have appointed princes, but I did not know it. With their silver and gold they have made idols for themselves, That they might be cut off. (Hosea 8:1–4, LSB2022)

Consider the Roman government in which the Romans Paul wrote to ended up executing Paul and Peter. Paul wasn't saying Rome was perfect, but their rule allowed Paul and other missionaries to travel between countries in the empire as if it were one country. Looking at Acts the Roman government tended to protect Paul from local and regional governments. Basically, government were the police enforcing the law. It wasn't like Judges where they were oppressed by every raiding party.

Another aspect is Paul was telling them not to seek overthrowing Rome to set up their own government. Christianity conquered Rome one person at a time, not by military action.

Every person is to be in subjection to the governing authorities. For there is no authority except from God, and those which exist have been appointed by God. Therefore whoever resists that authority has opposed the ordinance of God; and they who have opposed will receive condemnation upon themselves. For rulers are not a cause of fear for good behavior, but for evil. Do you want to have no fear of that authority? Do what is good, and you will have praise from the same; for it is a minister of God to you for good. But if you do what is evil, be afraid; for it does not bear the sword in vain, for it is a minister of God, an avenger who brings wrath on the one who practices evil. Therefore it is necessary to be in subjection, not only because of that wrath, but also because of conscience. (Romans 13:1–5, LSB2022)