This is basically what the Bible teaches, and it even teaches it in the dreaded Romans 13 that is so often misused to teach the exact opposite.
Romans 13:3 For rulers are not a terror to good conduct, but to bad. Would you have no fear of the one who is in authority? Then do what is good, and you will receive his approval, 4 for he is God's servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God's wrath on the wrongdoer.
It in no way will affect your Liberty to obey a ruler or authority that meets the definition you, or the Bible has put forward here. It would be as if there was no authority over you at all.
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