If this group is not anti-semitic as well as anti-fundamentalist, perhaps you will listen to a Jewish take on the meaning of render-unto-Caesar":
MaTiTIaHU 22:15-22
Then went the Pharisees, and took counsel how they might entangle Him in His talk.
And they sent out unto Him their disciples with the Herodians, saying, Rabbi, we know that Thou art True, and teachest the Way of Elohim in Truth, neither carest Thou for any man: for Thou regardest not the person of men.
Tell us therefore, What thinkest Thou? Is it Lawful to give tribute unto Caesar, or not?
But IaHUShUA perceived their wickedness, and said, Why tempt ye Me, ye hypocrites?
Shew Me the tribute money. And they brought unto Him a coin.
And He saith unto them, Whose is this image and superscription?
They say unto Him, Caesar's. Then saith He unto them, Render therefore unto Caesar the things which are Caesar's; and unto IaHUeH the things that are IaHUeH's.
When they had heard these words, they marvelled, and left Him, and went their way.
Luke 20:19-26 And the chief priests and the scribes the same hour sought to lay hands on Him; and they feared the people: for they perceived that He had spoken this parable against them.
And they watched Him, and sent forth spies, which should feign themselves just men, that they might take hold of His words, that so they might deliver Him unto the power and authority of the governor.
And they asked Him, saying, Rabbi, we know that Thou sayest and teachest rightly, neither acceptest Thou the person of any, but teachest the way of Elohim Truly:
Is it lawful for us to give tribute unto Caesar, or no?
If the earth is IaHUeH's and the fullness thereof, which it is! [Psalms 24] the metal in that coin belonged to IaHUeH. It was only the graven image that belonged to Caesar. And we know that a graven image amounts to NOTHING! ZERO! Which is exactly what is left if you take the metal out of a coin, or the paper and ink out of a hundred dollar bill!
These wicked men were trying to entrap Ha-MaShIaCh in His words, they were cunning and shrewd. They knew IaHUShUA taught IaHUeH's Law Rightly and Truly. Which Law explicitly forbids the worship of "mighty ones". They even revealed that they knew that it was transgression to submit to, serve, be afraid of or to otherwise worship Caesar "neither carest Thou for any man: for Thou regardest not the person of men".
These men knew that either way He answered, they would "have Him", helplessly trapped. If He said yes, He would be disobeying IaHUeH, in transgressing The Commandments.
If He said no, they would be able to turn Him in to the Roman authorities. They were amazed at His answer because they knew that what He said was "give nothing to Caesar" for He surely did not mean that whatever Caesar happened put his image on was therefore his. Of course they could not point that out in front of the people; for by doing so they would have fallen into their very own trap!
But He perceived their craftiness, and said unto them, Why tempt ye Me?
Shew Me a coin. Whose image and superscription hath it? They answered and said, Caesar's.
And He said unto them, Render therefore unto Caesar the things which be Caesar's, and unto IaHUeH the things which be IaHUeH's.
And they could not take hold of His words before the people: and they marveled at His answer, and held their peace.
render , v. Also 4_8 rendre, 6_7 Sc. rendir, ran(n)der.
[a. OF. rendre:---pop. Lat. *rendere (also found in med.L.) an alteration, on anal. of prendere, of class.L. reddere to give back, f. red- re- + dare to give.]
IV. 17. techn.
a. To melt (fat, metal etc.); to obtain or extract by melting; to clarify. Cf. rend v.2
Of course IaHUShUA knew the Law! these Words were the Words of His Father! IaHUeH! The Words He Himself spoke. He knew the importance of these Words and how they really apply. It was common knowledge in that time in Iahudea, that it was a transgression of the first Commandment to give loyal obedience to Caesar or any other worldly authority.
IaHUShUA Himself testified
MaTiTIaHU 5:17-19
Think not that I am come to destroy the Law, or the prophets: I am not come to destroy, but to fulfil.
For verily I say unto you, Till heaven and earth pass, one iod or one tittle shall in no wise pass from the Law, till all be fulfilled.
Whosoever therefore shall break one of these commandments least, and shall teach men so, he shall be called the least in the Kingdom of heaven: but whosoever shall do and teach them, the same shall be called great in the Kingdom of heaven.
Luke 16:13-17 No servant can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve IaHUeH and mammon.
And the Pharisees also, who were covetous, heard all these things: and they derided Him.
And He said unto them, Ye are they which justify yourselves before men; but IaHUeH knoweth your hearts: for that which is highly esteemed among men is abomination in the sight of IaHUeH.
The Law and the prophets were until IaHUChaNaN: since that time (if) the Kingdom of IaHUeH is preached, and every one presseth into it.
And it is easier for heaven and earth to pass, than one tittle of the Law to fail.
We are not telling you something new, but the same Word which was with you from the beginning; Love IaHUeH, obey His Commandments, and believe on the Name of His Son IaHUShUA Ha-MaShIaCh, who Loved you so much He died for your transgressions. If you Love Him, you will follow His instructions, which are the same Words IaHUeH spoke to MoSheH and all of His Prophets, before or since. This WORD does not change!!!
web address: http://www.iahushua.com/ST-RP/caesar.htm
see also JESUS OF NAZARETH, ILLEGAL-TAX PROTESTER, available without charge at http://www.jesus-on-taxes.com