Should you "render unto Caesar" anything that he, in his modern incarnation, demands?
Basically, to render unto Caesar what is Caesar's just means don't take, or keep, that which isn't yours. Don't steal. If you have someone else's property, give it back. Does your money automatically belong to the government just because someone passed a law permitting them to take it? Absolutely not. Should you pay for services you use, regardless of who provides them? Yes, you should. Should you be forced to pay for services you neither want nor need? If so, everyone should start sending me a monthly check for picking up litter, and for preaching liberty.
But what about submitting to government simply because it is the government? Do you have an obligation to obey every edict that comes from a government official simply because of his position? No.
In America no person, agency, or office is the governmental authority. The Constitution is. Those who refuse to abide by the letter and intent of that authority have no legitimate power over you. In fact by using coercion and violence on people who are harming no one else, and even against those who are doing "good work", they cause fear in good people and show themselves to be false authorities in violation of the Constitution.
Sure, the Constitution has its own problems, but as long as you choose to play the game, it is your rule book. If you seek political office, the Constitution is not to be "interpreted" to be more convenient for your ambitions. Once you violate any of its provisions, whether by trying to regulate immigration, by passing or enforcing "laws" against gun ownership or possession, or by regulating which substances people may introduce into their own bloodstream, you have lost all authority. No one has any obligation to honor or obey you any longer.
In America the Constitution was written to hobble the government, not to ensnare the people. Any ruling that goes against that higher power is a ruling that goes against the spirit of the Constitution- even if you approve. Those acts erode authority rather than enhancing it.
Every time this happens you can stop submitting, honoring, and complying- with a clear conscience.
If you feel called to support the earthly powers-that-be, don't misguidedly throw your support behind those who are in fact its worst enemy.