For a “caricature”, I have not seen too many libertarians diverge from it.
John Adams said that the US Constitution could not rule anyone who was not both moral and religious.
I'm a libertarian (and a Christian) and I heartily diverge from such extremes. So, too, do several of my libertarian friends, some of whom are only marginally Christian at best. Too much broad-brushing occurs here, just like the secular crowd likes to broad-brush the religious crowd regarding certain issues.
The nice thing about policy disagreements is that it's perfectly acceptable to express one's opposition to a given viewpoint, and even offer a well-reasoned rebuke in many cases.
Well-intentioned people who believe in Freedom will always have disagreements about war and peace, "foreign entanglements", hawks vs. doves, policing the world, the legitimate use of force, preemptive self-defense, what's in the national interest, and so on.
That's ultimately a healthy thing. As long as we each keep our eye on the goal, which is defending this Republic, we should accept the reality that there will be real disagreements even between well-meaning individuals and groups.
John Adams said that the US Constitution could not rule anyone who was not both moral and religious.
That's a valid opinion, but even some of his Founding Father peers undoubtedly disagreed with that sentiment.
Adams also harbored nostalgia for some of the vestiges of monarchy and aristocracy which echoed through the times in which he lived. Even his romantic notion of what the US Presidency should be displayed some of those lingering biases.
Notwithstanding the sentiments of our 2nd President, and although IMHO the Constitution doesn't really need to "rule" anyone (other than those with Tyrannical aims) I believe it is adequate to the task of governing a nation of widely varying religious, political, and secular paradigms, at least inasmuch as each maintains a profound appreciation for every individual's Unalienable right to Life, Liberty, and the Pursuit of Happiness.
Tyranny, in all its insidious forms, is the thing that is truly incompatible with the Constitution and Declaration. To the extent that there is tolerance (and even advocacy) of mob rule, demagoguery, unsustainable entitlements, corruption, and endless laws which oppress, impoverish, and even criminalize peacable citizens, that is where failures in government will occur, regardless of which rights are recognized or not, who is in power, or what the structural details might be.