"Government has no Right to hurt a hair of the head of an Atheist for his Opinions. Let him have a care of his Practices."
-- John Adams to John Quincy Adams, June 16, 1816. Adams Papers (microfilm), reel 432, Library of Congress, quoted in James H. Hutson, "The Founders on Religion," p. 20.
A reader asked whether any of America's Founders thought atheists ought to have rights. Yes, generally speaking they took Locke's notions of unalienable rights and extended them beyond Locke's initial conception which excluded atheists and Roman Catholics. Men of all religions or no religion at all had a right to freely practice their faith (consistent with the secular law). And unalienable rights further extended to some kind of substantive notion of equality. From my reading of the primary sources, it was an equal right to government benefits or to be free from religious establishments that hurt them in the pocketbook or in some tangible way. For this reason, Madison and Jefferson thought Patrick Henry's Virginia bill to provide financial aid to the "Christian religion" generally violated natural rights. They believed government could not aid one religion over another, or even aid "religion" over secular interests.
However, I endorse the conclusions of Philip Munoz and Justice Thomas that Jefferson and Madison believed if government provided aid on secular grounds (ala vouchers) such a natural right to equality would demand government not exclude religious interests from the secular program.
The other approach Washington, John Adams, and others endorsed held government could aid Christianity only, but because non-Christians by nature had unalienable rights, they were entitled to some kind of accommodation or exemption from programs that used tax dollars to benefit a religion in which they didn't believe.
As Washington put it, discussing the very same Patrick Henry's VA Bill that aided teachers of the "Christian religion":
I am not amongst the number of those who are so much alarmed at the thoughts of making people pay towards the support of that which they profess, if of the denomination of Christians; or declare themselves Jews, Mahomitans or otherwise, and thereby obtain proper relief. As the matter now stands, I wish an assessment had never been agitated, and as it has gone so far, that the Bill could die an easy death;... [My emphasis.]
Thus the general principle is the same: Men of any or no religion have an unalienable right to equality or "equal rights" in regard to religion. How government must act to secure those rights is something over which reasonable minds can differ. Regarding actual aid (meaning government funds) or legal penalties or privileges the answer seems quite simple: Government cannot treat atheists any different than theists or Christians and vice versa.
However, when it comes to government simply speaking or using its words, the matter is a bit more complicated because one can reasonably argue, "where's the harm?" If government says "under God," "under Jesus," "under Allah," "under no God," "under the Flying Green Spaghetti Monster," how do those words hurt such that it rises to the level of a constitutional issue?
When there are no actual religious exercises in which folks are expected to engage like "In God We Trust," I think the doctrine of ceremonial theism ought to trump (akin to government reading out loud the Declaration of Independence). I might even go further and say government can say whatever it wants on religious matters, including for instance Utah stating "we are the Mormon State," or Vermont stating "we deny the Trinity," or Alabama "Jesus is Lord," provided those governments still respect everyone's equal rights. Or it's possible that governments that officially make such sectarian overtures cannot possibly equally respect the rights of those who don't believe in them. But again, I would point out that though America's Founding theology is not Christian or even "biblical," it is generically theistic. If generic theism is sectarian, the Declaration and other natural rights documents make sectarian overtures.
What makes the pledge more difficult is that it involves an actual exercise in which all school children are expected to engage. As it currently stands, a long line of Supreme Court cases, notably West Virginia v. Barnett properly hold that students have a constitutional right not to pledge the flag, which means if an atheist student wants to keep her mouth shut when the class says "under God," sit down and not salute the flag or leave the room altogether she would have that right (this seems closer to the accommodation that George Washington would give).
I remember one Jehovah's Witness in middle school taking advantage of his rights ala Barnett; he sat down during the pledge and did stick out.
Perhaps, for a variety of reasons -- sticking out like a sore thumb, taunts, peer pressure -- that kind of accommodation is not sufficient. One commenter remarked that the "under God" in the pledge is like making atheists sit on the back of the bus. Is their analysis proper, or is this melodrama? My mind isn't made up; though I'm on the fence as a constitutional matter, as a policy matter, I'd remove the "under God" because it's disrespectful towards atheists and polytheists.