The earliest uses cited by the Oxford English Dictionary of the terms "Judeo–Christian" and "Judeo–Christianity" date to 1899 and 1910 respectively. Both terms appeared in discussions of theories of the emergence of Christianity, and with a different sense than the one common today. "Judeo–Christianity" here referred to the early Christian church, whose members were Jewish converts and still considered themselves part of the Jewish community.
It's ironic, isn't it? Jews very seldom refer to anything as 'Judeo-Christian'. In fact, most of us would rather not be involuntarily associated with Christianity to begin with. And many of us recognize that our beliefs have several points in common with Islam which differ from Christianity. So instead we tend to talk about the 'Abrahamic' faith traditions.
In my personal experience, most of the Christians who so blithely talk about 'Judeo-Christian' beliefs are actually quite ignorant of what Judaism does believe and how it regards its own Scriptures. And that's aside from the unsettling content of recent years (20 or so), when *some* Christians began to add an element of anti-Islamic bigotry to that label.
Supporting Israel does NOT! mean being anti-Muslim or anti-Arab to most of us who have relatives there (Some 20% of Israelis are Muslim/Arab, and yes they are full citizens). Bigotry of any kind is not 'supporting' anyone.
I can't understand why any knowledgable Muslim would take offense at the signs shown in the article linked in the OP. After all Allah (الله) is simply the Arabic translation of the word God. Therefore the signs that say In God We Trust, One Nation Under God, God Bless America, and God Shed His Grace On Thee could just as easily be written In Allah We Trust (ونحن على ثقة في الله), One Nation Under Allah (أمة واحدة تحت الله), Allah Bless America (رسول الله صلى الله أمريكا), and Allah Shed His Grace On Thee (تسليط الله على نعمته اليك) without changing the meaning at all.
It is possible that there are some Pagans or Atheists who could be offended, and their rights should be defended as much as anyone's.
Jefferson was either a Unitarian or a Deist depending on how one views his writings. For instance:
"The legitimate powers of government extend to such acts only as are injurious to others. But it does me no injury for my neighbor to say there are twenty gods or no God. It neither picks my pocket nor breaks my leg." ... Thomas Jefferson: Notes on the State of Virginia, 1781-1783
"I rejoice that in this blessed country of free inquiry and belief, which has surrendered its creed and conscience to neither kings nor priests, the genuine doctrine of one only God is reviving, and I trust that there is not a young man now living in the United States who will not die a Unitarian." --Thomas Jefferson (To Dr. Benjamin Waterhouse, June 26, 1822)
When he wrote "All Men Are Created Equal. They Are Endowed By Their Creator with certain inalienable rights" he was speaking of the deistic "first cause" that created the universe, not the Christian God. Jefferson was certainly no Christian. Otherwise he would not have taken his rasor to the New Testament and cut out all the mystery, miracle, and prophesy contained in it, leaving only the positive message given by Jesus. You can find the Jefferson Bible easily online.
Jefferson was also a strict Separationist who would abhor the idea of Christianity being taught in public schools.
To messers Nehemiah Dodge, Ephraim Robbins, & Stephen S. Nelson a committee of the Danbury Baptist association in the state of Connecticut.
The affectionate sentiments of esteem & approbation which you are so good as to express towards me, on behalf of the Danbury Baptist association, give me the highest satisfaction. my duties dictate a faithful & zealous pursuit of the interests of my constituents, and in proportion as they are persuaded of my fidelity to those duties, the discharge of them becomes more & more pleasing. Believing with you that religion is a matter which lies solely between man & his god, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, and not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should make no law respecting an establishment of religion, or prohibiting the free exercise thereof, thus building a wall of separation between church and state. [Congress thus inhibited from acts respecting religion, and the Executive authorised only to execute their acts, I have refrained from presenting even occasional performances of devotion presented indeed legally where an Executive is the legal head of a national church, but subject here, as religious exercises only to the voluntary regulations and discipline of each respective sect.] Adhering to this expression of the supreme will of the nation in behalf of the rights of conscience, I shall see with sincere satisfaction the progress of those sentiments which tend to restore to man all his natural rights, convinced he has no natural right in opposition to his social duties. I reciprocate your kind prayers for the protection and blessing of the common Father and creator of man, and tender you for yourselves and your religious association, assurances of my high respect & esteem.
(signed) Thomas Jefferson Jan.1.1802
"History, I believe, furnishes no example of a priest-ridden people maintaining a free civil government. This marks the lowest grade of ignorance of which their civil as well as religious leaders will always avail themselves for their own purposes." --Thomas Jefferson to Alexander von Humboldt, 1813.
from Thomas Jefferson's letter to his nephew, Peter Carr, concerning Peter's education, written from Paris on August 10, 1787.
4. Religion. Your reason is now mature enough to examine this object. In the first place, divest yourself of all bias in favor of novelty and singularity of opinion. Indulge them in any other subject rather than that of religion. It is too important, and the consequences of error may be too serious. On the other hand, shake off all the fears and servile prejudices, under which weak minds are servilely crouched. Fix reason firmly in her seat, and call to her tribunal every fact, every opinion. Question with boldness even the existence of a God; because, if there be one, he must more approve of the homage of reason, than that of blindfolded fear. You will naturally examine first, the religion of your own country. Read the Bible, then as you would read Livy or Tacitus. The facts which are within the ordinary course of nature, you will believe on the authority of the writer, as you do those of the same kind in Livy and Tacitus. The testimony of the writer weighs in their favor, in one scale, and their not being against the laws of nature, does not weigh against them. But those facts in the Bible which contradict the laws of nature, must be examined with more care, and under a variety of faces. Here you must recur to the pretensions of the writer to inspiration from God. Examine upon what evidence his pretensions are founded, and whether that evidence is so strong, as that its falsehood would be more improbable than a change in the laws of nature, in the case he relates. For example, in the book of Joshua, we are told, the sun stood still several hours. Were we to read that fact in Livy or Tacitus, we should class it with their showers of blood, speaking of statues, beasts, etc. But it is said, that the writer of that book was inspired. Examine, therefore, candidly, what evidence there is of his having been inspired. The pretension is entitled to your inquiry, because millions believe it. On the other hand, you are astronomer enough to know how contrary it is to the law of nature that a body revolving on its axis, as the earth does, should have stopped, should not, by that sudden stoppage, have prostrated animals, trees, buildings, and should after a certain time gave resumed its revolution, and that without a second general prostration. Is this arrest of the earth's motion, or the evidence which affirms it, most within the law of probabilities? You will next read the New Testament. It is the history of a personage called Jesus. Keep in your eye the opposite pretensions: 1, of those who say he was begotten by God, born of a virgin, suspended and reversed the laws of nature at will, and ascended bodily into heaven; and 2, of those who say he was a man of illegitimate birth, of a benevolent heart, enthusiastic mind, who set out without pretensions to divinity, ended in believing them, and was punished capitally for sedition, by being gibbeted, according to the Roman law, which punished the first commission of that offence by whipping, and the second by exile, or death "in furea"....
Do not be frightened from this inquiry by any fear of its consequences. If it ends in a belief that there is no God, you will find incitements to virtue in the comfort and pleasantness you feel in its exercise, and the love of others which it will procure you. If you find reason to believe there is a God, a consciousness that you are acting under his eye, and that he approves you, will be a vast additional incitement; if that there be a future state, the hope of a happy existence in that increases the appetite to deserve it; if that Jesus was also a God, you will be comforted by a belief of his aid and love. In fine, I repeat, you must lay aside all prejudice on both sides, and neither believe nor reject anything, because any other persons, or description of persons, have rejected or believed it. Your own reason is the only oracle given you by heaven, and you are answerable, not for the rightness, but uprightness of the decision. I forgot to observe, when speaking of the New Testament, that you should read all the histories of Christ, as well of those whom a council of ecclesiastics have decided for us, to be Pseudo-evangelists, as those they named Evangelists. Because these Pseudo-evangelists pretended to inspiration, as much as the others, and you are to judge their pretensions by your own reason, and not by the reason of those ecclesiastics. Most of these are lost. There are some, however, still extant, collected by Fabricius, which I will endeavor to get and send you.
"The right of voting for representatives is the primary right by which other rights are protected. To take away this right is to reduce a man to slavery, for slavery consists in being subject to the will of another, and he that has not a vote in the election of representatives is in this case." Thomas Paine: Dissertation on First Principles of Government (July 1795)