I don't know that Jesus' intention with that "Render unto Caesar's" verse was that everyone should always obey the government and the law in every case. I mean, it was illegal to be a Christian at different times in different places so, by that logic, should Christians have abandoned their faith because it was a sin to go against the law of the land? Just some food for thought...
Perhaps it's good to look at the passage in context:
All of you must be willing to obey completely those who rule over you. There are no authorities except the ones God has chosen. Those who now rule have been chosen by God. So when you oppose the authorities, you are opposing those whom God has appointed. Those who do that will be judged.If you do what is right, you won't need to be afraid of your rulers. But watch out if you do what is wrong! You don't want to be afraid of those in authority, do you? Then do what is right. The one in authority will praise you. He serves God and will do you good. But if you do wrong, watch out! The ruler doesn't carry a sword for no reason at all. He serves God. And God is carrying out his anger through him. The ruler punishes anyone who does wrong.
You must obey the authorities. Then you will not be punished. You must also obey them because you know it is right.
That's also why you pay taxes. The authorities serve God. Ruling takes up all their time. Give to everyone what you owe. Do you owe taxes? Then pay them. Do you owe anything else to the government? Then pay it. Do you owe respect? Then give it. Do you owe honor? Then show it.
With that in mind we can also look at Acts 5 that says as long as the law of the land does not contradict the law of God, we are bound to obey the law of the land. As soon as the law of the land contradicts God's command, we are to disobey the law of the land and obey God's law (which sometimes may carry consequences as well, just look at Peter and John). So no they should not have abandoned their faith b/c (as in Acts 5) God and God's law come first, even though one might suffer terribly for it by the law of the land.