Here we hit one of the big stumbling blocks that Christian tax resisters have run into.  The New Testament is distressingly explicit, in Romans 13:

Everyone must submit himself to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. Consequently, he who rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves.... [I]t is necessary to submit to the authorities, not only because of possible punishment but also because of conscience. This is also why you pay taxes, for the authorities are God's servants, who give their full time to governing. Give everyone what you owe him: If you owe taxes, pay taxes; if revenue, then revenue; if respect, then respect; if honor, then honor.

If Jesus wanted us to know that we should resist taxes to governments that were going to apply the tax money in sinful ways, he was given every opportunity to make this clear when he was asked: "Is it right to pay taxes to Caesar or not?"  Instead, he responded with the koan "Give to Caesar what is Caesar's, and to God what is God's" which confused everybody at the time, and the meaning of which continues to defy consensus today.

The best the resisters could come up with to justify their position was either a confidently asserted, if somewhat strained reading of the "Give to Caesar" koan (one war tax resister insisted that Jesus delivered his koan during a time of peace in the Roman Empire, so Jesus was by no means countenancing war taxes), or the story from Acts 5 in which the apostles defied the law and continued to preach the gospel according to God's explicit command.  Asked to explain themselves,

Peter and the other apostles replied: "We must obey God rather than men!"

Most Christian tax resisters took the "Give to Caesar" koan and certainly the Romans passage to mean that God does indeed command us to pay taxes, even to unjust governments, but took the Acts "We must obey God rather than men" statement to provide an occasional override:  Essentially "render unto Caesar and submit to the government, unless that means disobeying God."

T.S. Grimké put it this way:

[If the ruler] require me to pay taxes, although one object of the taxes be the support of idolatry, or the waging of war, I comply, simply because he has a clear right to levy taxes, and the responsibility of applying them is with him, not with me. He is lawfully possessed of the power on the principle of civil obedience, as taught us in the New Testament; taxes are among the usual and necessary instruments for the administration of government; the use to which he shall apply them, is not my province, but his: he requires nothing unlawful of me, and therefore I comply.

Here then is the distinction. If he commands what is unlawful, as a means for the attainment of even a lawful end, I refuse obedience. But if he commands what is lawful, intending when the command has been performed by me, to employ the fruit of my obedience in the accomplishment of unlawful purposes in which I have no hand, I obey, because he requires of me only what is rightful. I have nothing to do with his motive or his object.

would illustrate this by the case of a debt. I am indebted to another. He demands payment. I am not at liberty to refuse, because I happen to know, or have reason to believe that he will employ the money, when paid, for unlawful or immoral purposes. This follows from the principle already stated. My duty is very clear, to pay the debt: the use of the money, when paid, is at once his right and responsibility. This may be aptly illustrated by a modification of the case stated. I am indebted to another; but the debt is not due. He calls for payment, not having a right to do so, and I happen to know, that his reason for wishing the money then, is to make an improper use of it. I am bound to refuse; because not being bound to pay then, I am volunteering to grant a favor, knowing that it will be abused.

On the same principle I can conscientiously pay taxes, knowing, that among other objects, the public money will be applied to pay judges and jurors for trying and condemning criminals to capital punishment; to pay the salary of the president of a college, who teaches that public prayer is unchristian, and the clergy a set of impostors; or to pay the expenses of war. This seems to me the only safe and wise principle, and it furnishes a suitable criterion for civil obedience.

[However, if the] magistrate, instead of a general tax law divides the taxes, and lays on the advocates of Peace the war tax. They cannot conscientiously pay it; because they are thus made the sole and direct instrument of carrying on the war, and without their compliance, it must be at a stand. ...

...Obedience is due to the civil magistrate, not as a duty to society, but as a duty to God. God only can then lawfully fix the land-marks of that duty.

This was also Edward Swaine's argument against tax resistance by nonconformist Christians against government support for establishment churches.  And he was unafraid to take his argument to its logical ends:

If Cæsar say “Give me money,” we must give it; for God has nowhere said “Do not give Cæsar money,” or “Do not give Cæsar money without satisfaction that he will properly apply it.” If Cæsar say “Do not preach,” Paul must refuse obedience, for Christ has said to him “preach!” If Cæsar say to us, “Go to the North Pole”—or “wear a cocked hat”—we must do so; for God has not claimed our obedience to the contrary. He has not said, “Do not go to the North Pole” or “go only where you please.” He has not said, “Do not wear a cocked hat,” or “wear only what you like,” Those things, then, concerning which God has claimed nothing of us, we must render unto Cæsar.

Swaine draws the line in this way:

God says to us in effect... If [Caesar] should say to you... “I resolve to establish the worship of Baal for the good of the Empire,” and to levy a tax for that purpose, the resources of the State are his, and you are bound to render the tax. But, if he should say I hold it to be for the good of the land, that every one acknowledge Baal to be God, and therefore require the payment of the tax to be accompanied by a recognition by the payers of the godhead of Baal, you are bound, while you pay the tax, to refuse the recognition, though impaling or burning be the penalty. Or, if the tax be collected under an enactment that every one who pays shall be considered as offering to Baal, you are bound to refuse the payment, for to pay in such case would be equivalent to worship, and a rendering to Cæsar of that which is God’s. But I do not justify your refusal of taxes, because they may be levied for a purpose that my law condemns. He who violates my law must answer, and that is not you who pay the tax, but he who levies it if a bad one. It is he who misapplies the National Funds, not you who had no rightful command over them to apply or misapply.

You have no responsibility, and violate none of God's laws, if your tax dollars are spent in sinful ways, according to Swaine, because "the tax-gatherer comes... not for a contribution, or subscription, or aid, but for property no longer the subject’s to give or to withhold, and no longer under his rightful control..."

Taxes for bad objects are to be paid, not because we can be excused for helping evil by any voluntary act, that we are morally free to forbear, nor because the payment of such taxes will not help evil, for it will help evil, just as much as the payment of a debt to one who is going to misapply the money will help the evil,—but because the tax is not the subject’s any more than the debt is the debtor’s to help with or to withhold. The payment therefore is his duty, for he is not morally free to decline it, although it will help evil.

...segue to tax as debt...