We are not all the same 'deep down,' and we don't all want the same things. You say you value peace and social harmony? So do I. But some are bellicose right out of the box. They love war and thrive on conflict, and not just verbally.
It is dangerous to assume that others are like we are. (I am thinking right now of a very loving and lovable female neighbor who makes that dangerous assumption: she has a 'Coexist' sticker affixed to her bumper.)
Liberal 'projectionism' — to give it a name— can get your irenic self killed.
As desirable a desideratum as peaceful coexistence is, it is inconsistent with totalitarian systems. This is why communism and Christianity cannot coexist assuming that they remain true to their defining principles. (Or at least they cannot coexist in the same geographical area over the long term.) They are mutually exclusive worldviews. And of course they are not just comprehensive views of the world and the people in it, but practical systems of prescriptions and proscriptions oriented toward the guidance of human action. The actional side is paramount in both systems. Old Karl said that the philosophers had variously interpreted the world when the point was to change it. (Karl Marx, Theses on Feuerbach, #11). A serious Christian could say that the philosophers had variously theorized and speculated when the unum necessarium was the salvation of one's immortal soul. "For what doth it profit a man, if he gain the whole world, and suffer the loss of his own soul?" (Matthew 16-26) A library of learned disquisitions on the nature of the soul is of no avail if one in the end suffers its loss.
Christianity and Islam are also quite obviously mutually exclusive on both doctrinal and practical planes. Note that both in their ideological purity are totalitarian at the personal level whether or not they are also totalitarian at the political level. (Christianity in the West has of course been liberalized to a great extent and is thus no longer ideologically pure.) The two in their pure forms make a total claim on the lives of their adherents. That is what I mean when I say that they are both personally totalitarian. This is not a problem if each remains personally totalitarian and neither becomes politically totalitarian. They cannot peacefully coexist in the same geographical area over the long term if either seeks political control over the whole area in accordance with the principles of the respective religions. The Muslim says to ‘the infidel’: either convert to the true faith, or accept dhimmitude, or be put to the sword. That, for a Christian, is indeed a trilemma: you will be impaled on one of three horns, but you are free to choose which one. You are not free not to choose one.
Can classical liberalism, the touchstone of which is toleration, coexist with any totalitarian ideology, religious or secular, if that ideology is enforced on all by the power of the state? No again. The classical liberal can and will tolerate any ideology as long as it respects the principle of toleration; it cannot, however, tolerate the rejection of this very principle, the principle that defines it. The rub, for the political totalitarian, is that if he accepts the principle of toleration, he can no longer remain politically totalitarian: he will have to accept church/mosque/temple - state separation. Now leftism is not a religion, but it is very much like a religion, so much so that many have an irresistible tendency to call it a religion. This tendency ought to be resisted by those who value terminological precision. We may, however, call leftism a totalitarian quasi-religion or a totalitarian ersatz religion. Leftism is not classically liberal. Classical liberalism and totalitarian systems are mutually exclusive.
So just as we need church-state separation and mosque-state separation, we need Left-state separation. Just as we need to oppose theocracy, whether Jewish, Christian, or Muslim, we need to oppose ‘leftocracy’ which is to say, government animated and driven by leftist principles.
So where does this leave us? There can be no peaceful coexistence in one and the same geographical area over the long term except under classical liberalism. For classical liberalism alone is tolerant of deep differences and is alone respectful of our equally deep ignorance of the ultimate truth about the ultimate matters. Why must we be tolerant? Because we do not know. The classical liberal is keenly aware of the evil in the human heart and of the necessity of limited government and dispersed power. So he is justified in making war against fanaticism, one-sidedness, and totalitarian systems of government whether theocratic or 'leftocratic.' It would not be a war of extermination but one of limitation. It would also be limited to one's geographical area and not promoted abroad to impose the values of classical liberalism on the benighted tribalists of the Middle East and elsewhere.
Finally, can American conservatism and the ideology of the Democrat Party in its contemporary incarnation peacefully coexist? Obviously not, which is why there is a battle for the soul of America. Either we defeat the totalitarian Left or we face a nasty trilemmatic trident: acquiesce and convert; or accept dhimmitude; or be cancelled in one’s livelihood and then eventually in one's life.