The NT teaching was not, "Honor and respect only those rulers you deem worthy of respect." The command was simply to honor all who are in authority, not for everything they did or were doing, but because of the positions of authority they held in the earth. I advocate for keeping Him on the throne through our behavior, which should be a reflection of truly living out our faith before men in the earth.
Kinda like these, eh?:
"Let every soul be subject unto the higher powers. For there is no power but of God: the powers
that be are ordained of God. Whosoever therefore resisteth the power, resisteth the ordinance of
God: and they that resist shall receive to themselves damnation.
For rulers are not a terror to good works, but to the evil. Wilt thou then not be afraid of the power?
do that which is good, and thou shalt have praise of the same: For he is the minister of God to thee
for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the
minister of God, a revenger to execute wrath upon him that doeth evil.
Wherefore ye must needs be subject, not only for wrath, but also for conscience sake. For for this
cause pay ye tribute also: for they are God’s ministers, attending continually upon this very thing.
Render therefore to all their dues: tribute to whom tribute is due; custom to whom
custom; fear to whom fear; honour to whom honour." (Romans 13:1-7 AV)
+
"I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of
thanks, be made for all men; For kings, and for all that are in authority; that we may
lead a quiet and peaceable life in all godliness and honesty.
[ slandering those in authority? ]
For this is good and acceptable in The Sight of God ( Jesus Christ ) our Saviour;
Who will have all men to be saved, and to come unto the knowledge of The Truth"
(1 Timothy 2:1-3 AV)
Amen.